Question 1

Find the zeroes of the functions algebraically. 
$f ( x ) = \frac { x ^ { 2 } - 14 x + 48 } { 7 x }$  
A) $x = - 8 , x = - 6 , x = \frac { 1 } { 7 }$
B) $x = 8 , x = 6$
C)  $x = - 8 , x = - 6$
D) $x = \frac { 1 } { 7 }$
E) $x = 8 , x = 6 , x = \frac { 1 } { 7 }$

Accepted Answer

To find the zeroes of the function, set $f(x) = 0$ and solve for $x$. The denominator $7x$ does not affect the zeroes of the numerator, but note that $x$ cannot be $0$ because of the division by $x$. Solving $x^2 - 14x + 48 = 0$ using factoring or the quadratic formula gives $x = 8$ and $x = 6$. The option $x = \frac{1}{7}$ is incorrect because it does not satisfy the equation $x^2 - 14x + 48 = 0$.

Question 2

Use the Vertical Line Test to determine in which of the graphs y is not a function of x. A)All of the choices (A, B, C, and D) represent functions. B) x² + y²= 16 C) $y = x ^ { 2 } + 2 x - 3$ D) $y = x ^ { 3 } - 2$ E) $y = \frac { 1 } { x }$

Accepted Answer

The answer of Use the Vertical Line Test to determine...

Question 3

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​
(4a, 6b)
​
A)​(-4a, -6b)
B)​(-4a, 6b)
C)​(4a, -6b)
D)​(4a, 6b)
E)None of the above

Accepted Answer

Since the function is odd, we know that $f(-x)=-f(x)$ for any $x$ in the domain of $f$. Therefore, if $(4a,6b)$ is on the graph of $f$, then $(-4a,-6b)$ must also be on the graph of $f$, since $f(-4a)=-f(4a)$ and $f(-4a, -6b)=-f(4a,6b)$. Thus, the answer is choice A.

Question 4

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. 
 $f ( x ) = 6 x ^ { 2 } - 12 x + 6$  
A) increasing on (-$\infty$, $\infty$)
B)descreasing on (-$\infty$, 1)increasing on (1, $\infty$)
C) increasing on (-$\infty$, 1)descreasing on (1, $\infty$)
D) descreasing on (-$\infty$, $\infty$)
E)descreasing on (1, 1)increasing on (1, $\infty$)

Accepted Answer

The function $f(x) = 6x^2 - 12x + 6$ is a quadratic function with a positive leading coefficient (6), indicating that it opens upwards. The vertex of this parabola, found by using the formula $-\frac{b}{2a}$, is at $x = 1$. This means the function is decreasing before $x = 1$ and increasing after $x = 1$.

Question 5

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. ​
F(x) = 5 - x
​
A)​  ​(∞, -5]
B)​  ​​(-∞, -5]
C)​  ​​(∞, 5]
D)​  ​​(-∞, 5]
E)​  ​​​(-∞, 5]

Accepted Answer

The answer of Select the graph of the given function...

Question 6

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$
A)relative maximum: (2.58, 0.39)relative minimum: (7.27, -1.72)
B)relative maximum: (0.39, 2.58)relative minimum: (-1.72, 7.27)
C)relative maximum: (-1.72, 7.27)relative minimum: (0.39, 2.58)
D)relative maximum: (7.27, -1.72)relative minimum: (2.58, 0.39)
E)relative maximum: (2.58, 28.33)relative minimum: (7.27, 478.41)

Accepted Answer

To find the relative maximum and minimum of the function $f(x) = x^3 + 2x^2 - 2x + 3$, we first find its derivative $f'(x) = 3x^2 + 4x - 2$ and solve $f'(x) = 0$ to find critical points. Solving this gives $x \approx -1.72$ and $x \approx 0.39$. Using the second derivative test or analyzing the sign changes of $f'(x)$ around these points, we can determine that $x \approx -1.72$ corresponds to a relative maximum and $x \approx 0.39$ to a relative minimum. Substituting these $x$ values back into $f(x)$ gives the respective $y$ values, leading to the correct answer.

Question 7

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. F(x) = 16 - x² A) [-4, -4] B) [-4, 4] C) [-4, -4] D) [4, -4] E) [-4, 4]

Accepted Answer

The graph of the function is a downward-facing parabola with vertex at (0,16) and opens downwards. The interval for which f(x) ≥ 0 is [-4, 4] because this is the interval where the graph is above or on the x-axis.

Question 8

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function. A)s = 16t² + 60 B)s = -16t² - 60 C)s = 16t² - 60 D)s = -16t² + 60 E)s = -16t² + 60t

Accepted Answer

The position equation for the given situation is:
s = -16t^2 + vt + s0
where s0 = 60 (since the object is dropped from a height of 60 feet)
and v = 0 (since the object is dropped and not thrown or given an initial velocity)

So, the equation becomes:
s = -16t^2 + 60

Comparing this equation with the given choices, we can see that choice D matches the equation. Hence, the answer is D.

Question 9

Use a graphing utility to graph the function and find the zeroes of the function. 
 $f ( x ) = 7 - \frac { 3 } { x }$  
A) $x = \frac { 3 } { 7 }$
B) $x = - \frac { 3 } { 7 }$
C) $x = \frac { 7 } { 3 }$
D)  $x = - \frac { 7 } { 3 }$
E)no real zeroes

Accepted Answer

The zero of the function is the x-intercept of the graph, which is approximately $x = \frac { 3 } { 7 }$.

Question 10

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​
(8, -7)
​
A)(8, 7)
B)(8, -7)​
C)(-8, -7)​
D)(-8, 7)​
E)None of the above

Accepted Answer

For an odd function, $f(-x) = -f(x)$. Given a point (8, -7) on the graph, the corresponding point for $-x$ would be $(-8, 7)$, maintaining the property of odd functions.

Question 11

Graph the function and determine the interval(s) for which f (x) $\ge$0. $$f ( x ) = - x ^ { 2 } - 2 x$$ 
A) $( - \infty , - 2 ) \cup ( 0 , \infty )$
B) $( - 2,0 )$
C) $[ - 2,0 ]$
D){-2}
E) $( - \infty , - 2 ] \cup [ 0 , \infty )$

Accepted Answer

The answer of Graph the function and determine the interval(s)...

Question 12

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function. A)s = -16t² + 90t B)s = -16t² - 90t C)s = 16t² + 90t D)s = 16t² - 90t E)s = -16t² + 90t + 8

Accepted Answer

The answer of An object is thrown upward from ground...

Question 13

Determine the intervals over which the function is increasing, decreasing, or constant. $$f ( x ) = \left\{ \begin{array} { l } 
- x ^ { 2 } , x < 1 \
x ^ { 2 } - 2 x + 2 , x \geq 1
\end{array} \right.$$ 
A) constant on (-$\infty$, 0)increasing on (0, $\infty$) 
B)increasing on (-$\infty$, 0), (1, $\infty$)descreasing on (0, 1)
C) constant on (-$\infty$, 1)increasing on (1, $\infty$) 
D) constant on (-$\infty$, 1)descreasing on (1, $\infty$) 
E) constant on (-$\infty$, 0)descreasing on (0, 1)

Accepted Answer

The answer of Determine the intervals over which the function...

Question 14

Select the graph of the given function and determine the interval(s) for which f(x)$\ge$ 0. 
 $f ( x ) = - ( 6 + | x | )$  
A)    f(x) > 6 for all x.
B)    f(x) < 0 for all x.
C)    f(x) $\le$  0 for all x.
D)    f(x)$\ge$  0 for all x.
E)    f(x) > 0 for all x.

Accepted Answer

The answer of Select the graph of the given function...

Question 15

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. ​
(-x, y)
​
A)(-x, -y)
B)(x, -y)
C)(-x, y)
D)(x, y)
E)None of the above

Accepted Answer

For an even function, f(x) = f(-x). This means if (-x, y) is a point on the graph, then (x, y) must also be a point on the graph, because the function's value at x and -x is the same.

Question 16

An object is thrown upward from a height of 8 feet at a velocity of 72 feet per second. Use the position equation s = -16t₂ + v₀t + s₀ to select a function that represents the situation and select the graph of the function. A) s = -16t² - 72t + 8 B) s = -16t² + 72t C) s = -16t² + 72t - 8 D)s = -16t² + 72t + 8 E) s = -16t² - 72t - 8

Accepted Answer

Using the position equation s = -16t^2 + vt + s0, where v is the initial velocity and s0 is the initial height, we can plug in the given values and simplify:
s = -16t^2 + 72t + 8
This matches option D, so the answer is D. The graph of this function would be a downward-facing parabola opening up, since the coefficient of t^2 is negative. The vertex of the parabola would represent the maximum height reached by the object.

Question 17

Find the zeroes of the functions algebraically. 
 $f ( x ) = \sqrt { 5 x } - 9$  
A) $x = \pm \frac { 9 } { 5 }$
B) $x = \pm \frac { 81 } { 5 }$
C)  $x = \frac { 9 } { 5 }$
D)  $x = \frac { 81 } { 5 }$
E) no real zeroes

Accepted Answer

To find the zeroes of the function $f(x) = \sqrt{5x} - 9$, we set it equal to zero and solve for $x$: $\sqrt{5x} - 9 = 0$. Adding 9 to both sides gives $\sqrt{5x} = 9$. Squaring both sides to eliminate the square root gives $5x = 81$. Dividing by 5 gives $x = \frac{81}{5}$.

Question 18

Select the graph of the given function and determine the interval(s) for which f(x) $\ge$0. 
 $f ( x ) = \sqrt { x - 2 }$  
A)    (-$\infty$, 2]
B)    [-2, $\infty$)
C)    [-2, 2)
D)   [2, $\infty$)
E)    [-2, $\infty$)

Accepted Answer

The answer of Select the graph of the given function...

Question 19

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function. A)s = -16t² + 80 - 6.4 B)s = -16t² + 80t C)s = -16t² - 80t - 6.4 D)s = -16t² - 80t + 6.4 E)s = -16t² + 80t + 6.4

Accepted Answer

The answer of An object is thrown upward from a...

Question 20

An object is dropped from a height of 15 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function. A)s = -16t² + 15t B)s = -16t² + 15 C)s = -16t² - 15t D)s = 16t² + 15 E)s = -16t² - 15

Accepted Answer

- The position equation for an object dropped from a height of 15 feet is s = -16t^2 + 15. 
- This matches option B: s = -16t^2 + 15. 
- Option A has an extra t term. 
- Option C and E have a negative coefficient for the t term, which means the object is moving downwards with increasing time, but in reality, the object is only moving downwards due to gravity. 
- Option D has a positive coefficient for the t term, which means the object is moving upwards with increasing time, but again, in reality, the object is only moving downwards due to gravity.

Quiz 1: Functions and Their Graphs

Find the zeroes of the functions algebraically. $f ( x ) = \frac { x ^ { 2 } - 14 x + 48 } { 7 x }$

Use the Vertical Line Test to determine in which of the graphs y is not a function of x.

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (4a, 6b)

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = 6 x ^ { 2 } - 12 x + 6$

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. F(x) = 5 - x

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. F(x) = 16 - x²

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.

Use a graphing utility to graph the function and find the zeroes of the function. $f ( x ) = 7 - \frac { 3 } { x }$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (8, -7)

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Select the graph of the given function and determine the interval(s) for which f(x) $\ge$ 0. $f ( x ) = - ( 6 + | x | )$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. (-x, y)

An object is thrown upward from a height of 8 feet at a velocity of 72 feet per second. Use the position equation s = -16t₂ + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Find the zeroes of the functions algebraically. $f ( x ) = \sqrt { 5 x } - 9$

Select the graph of the given function and determine the interval(s) for which f(x) $\ge$ 0. $f ( x ) = \sqrt { x - 2 }$

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

An object is dropped from a height of 15 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.

Quiz 1: Functions and Their Graphs

Find the zeroes of the functions algebraically. f(x) =x2−14x+487xf ( x ) = \frac { x ^ { 2 } - 14 x + 48 } { 7 x }f(x) =7xx2−14x+48​

Use the Vertical Line Test to determine in which of the graphs y is not a function of x.

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​ (4a, 6b) ​

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. f(x) =6x2−12x+6f ( x ) = 6 x ^ { 2 } - 12 x + 6f(x) =6x2−12x+6

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. ​ F(x) = 5 - x ​

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f(x) =x3+2x2−2x+3f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3f(x) =x3+2x2−2x+3

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. ​ F(x) = 16 - x2 ​

An object is dropped from a height of 60 feet. Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and select the graph of the function. ​

Use a graphing utility to graph the function and find the zeroes of the function. f(x) =7−3xf ( x ) = 7 - \frac { 3 } { x }f(x) =7−x3​

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. ​ (8, -7) ​

Graph the function and determine the interval(s) for which f (x) ≥\ge≥ 0. f(x) =−x2−2xf ( x ) = - x ^ { 2 } - 2 xf(x) =−x2−2x

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t2 + v0t + s0 to select a function that represents the situation and select the graph of the function. ​

Determine the intervals over which the function is increasing, decreasing, or constant. f(x) ={−x2,x<1x2−2x+2,x≥1f ( x ) = \left\{ \begin{array} { l } - x ^ { 2 } , x < 1 \\x ^ { 2 } - 2 x + 2 , x \geq 1\end{array} \right.f(x) ={−x2,x<1x2−2x+2,x≥1​

Select the graph of the given function and determine the interval(s) for which f(x) ≥\ge≥ 0. f(x) =−(6+∣x∣) f ( x ) = - ( 6 + | x | ) f(x) =−(6+∣x∣)

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. ​ (-x, y) ​

An object is thrown upward from a height of 8 feet at a velocity of 72 feet per second. Use the position equation s = -16t2 + v0t + s0 to select a function that represents the situation and select the graph of the function. ​

Find the zeroes of the functions algebraically. f(x) =5x−9f ( x ) = \sqrt { 5 x } - 9f(x) =5x​−9

Select the graph of the given function and determine the interval(s) for which f(x) ≥\ge≥ 0. f(x) =x−2f ( x ) = \sqrt { x - 2 }f(x) =x−2​

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t2 + v0t + s0 to select a function that represents the situation and select the graph of the function. ​

An object is dropped from a height of 15 feet. Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and select the graph of the function. ​

Find the zeroes of the functions algebraically. $f ( x ) = \frac { x ^ { 2 } - 14 x + 48 } { 7 x }$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (4a, 6b)

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = 6 x ^ { 2 } - 12 x + 6$

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. F(x) = 5 - x

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 2 x + 3$

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. F(x) = 16 - x²

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.

Use a graphing utility to graph the function and find the zeroes of the function. $f ( x ) = 7 - \frac { 3 } { x }$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. (8, -7)

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Select the graph of the given function and determine the interval(s) for which f(x) $\ge$ 0. $f ( x ) = - ( 6 + | x | )$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. (-x, y)

An object is thrown upward from a height of 8 feet at a velocity of 72 feet per second. Use the position equation s = -16t₂ + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Find the zeroes of the functions algebraically. $f ( x ) = \sqrt { 5 x } - 9$

Select the graph of the given function and determine the interval(s) for which f(x) $\ge$ 0. $f ( x ) = \sqrt { x - 2 }$

An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

An object is dropped from a height of 15 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.