Question 1

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, if (x, y) is on the graph, then (-x, -y) is also on the graph. Given (8, -7), the second point is (-8, 7).

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 it has symmetry with respect to the origin. This means that for any point (x,y) on the graph of the function, (-x,-y) must also be on the graph.

In this case, we are given the point (4a, 6b) on the graph of the function. So, using the symmetry property for an odd function, we can say that (-4a,-6b) must also be on the graph.

Therefore, the correct choice is A) (-4a,-6b).

Question 4

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 unless $x = 0$, which would make the function undefined rather than zero. So, focus on the numerator: $x^2 - 14x + 48 = 0$. Factoring this quadratic equation gives $(x - 8)(x - 6) = 0$, leading to the solutions $x = 8$ and $x = 6$.

Question 5

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 6

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. ​
(4,3)
​
A)(-4,-3)
B)(-4,3)
C)(4,3) ​
D)​(4,-3) ​
E)None of the above

Accepted Answer

For an even function, f(x) = f(-x). This means that if (4,3) is a point on the graph, then (-4,3) must also be a point on the graph because the y-value remains the same when the x-value is negated.

Question 7

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 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 given equation for position is s = -16t^2 + vt + s0, where s0 is the initial position (in this case, 60 feet) and v is the initial velocity (in this case, 0 since the object is simply dropped). Plugging in these values gives us s = -16t^2 + 60, which matches option D.

Question 9

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 10

The number of lumens (time rate of flow of light)L from a fluorescent lamp can be approximated by the model L = -0.294x² + 97.744x - 664.875, 20 ≤ x ≤ 90 Where x is the wattage of the lamp. Use a graphing utility to select the graph of the function.Use the graph to estimate the wattage necessary to obtain 2400 lumens. A) 40W B) 30W C) 45W D) 25W E) 35W

Accepted Answer

The answer of The number of lumens (time rate of...

Question 11

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

Accepted Answer

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

Question 12

Select the graph of the function and determine whether it is even,odd,or neither.? $$g ( t ) = \sqrt [ 3 ] { t - 4 }$$ ?
A)?  Even
B)?  Odd
C)?  Neither
D)?  Even
E)?  Odd

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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 this situation is s = -16t^2 + v0t + s0, where t represents time, v0 represents the initial velocity, and s0 represents the initial position. Since the object is dropped (i.e. it starts from rest), v0 = 0. And since the object is dropped from a height of 15 feet, s0 = 15. Therefore, the function that represents the situation is s = -16t^2 + 15. This is equivalent to choice B.

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 is the same as its value at -x.

Question 16

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 in option E shows that the function is equal to 0 at x = -4 and x = 4, and is positive for all values of x between -4 and 4. Therefore, the interval for which f(x) is greater than or equal to 0 is [-4,4].

Options A, B, C, and D do not show the correct shape of the graph or the correct intervals for f(x) to be greater than or equal to 0.

Question 17

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.? $\left( - \frac { 1 } { 2 } , 5 \right)$ ?
A) $\left( - \frac { 1 } { 2 } , - 5 \right)$
B) $\left( \frac { 1 } { 2 } , 5 \right)$ ?
C) $\left( \frac { 1 } { 2 } , - 5 \right)$ ?
D) $\left( - \frac { 1 } { 2 } , 5 \right)$ ?
E)None of the above

Accepted Answer

For an even function, $f(x) = f(-x)$. Given a point $\left( - \frac { 1 } { 2 } , 5 \right)$, its symmetric point across the y-axis would be $\left( \frac { 1 } { 2 } , 5 \right)$, maintaining the same y-value but with the opposite x-value.

Question 18

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.? $\left( - \frac { 9 } { 7 } , - 4 \right)$ ?
A) $\left( \frac { 9 } { 7 } , 4 \right)$
B)? $\left( - \frac { 9 } { 7 } , 4 \right)$
C)? $\left( - \frac { 9 } { 7 } , - 4 \right)$
D)? $\left( \frac { 9 } { 7 } , - 4 \right)$
E)None of the above

Accepted Answer

For an odd function, $f(-x) = -f(x)$. Given a point $\left( - \frac { 9 } { 7 } , - 4 \right)$, its symmetric point across the origin would be $\left( \frac { 9 } { 7 } , 4 \right)$, which satisfies the property of odd functions.

Question 19

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

The position equation for this scenario is: 
s = -16t^2 + vt + s0, where 
s0 = initial height = 8 
v = initial velocity = 72 
We can substitute these values into the equation to get: 
s = -16t^2 + 72t + 8 
This matches choice D. The graph of this equation should be a parabolic shape opening downwards, since the object is thrown upwards and then falls back down due to gravity.

Question 20

Select the graph of the function and determine whether it is even,odd,or neither. ​
F(x)= |x + 6|
​
A)​  Even
B)​  Odd
C)​  Neither
D)​  Odd
E)​  Even

Accepted Answer

The graph of f(x) = |x + 6| is a V-shaped graph with vertex (-6,0) and the arms opening upward and downward. Since the function is not symmetric about the y-axis (which would make it even) and the graph does not have rotational symmetry of 180 degrees about the origin (which would make it odd), it is neither even nor odd. Therefore, the correct choice is C.

Quiz 5: Analyzing Graphs of Functions

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)

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)

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

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.

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. (4,3)

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

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.

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.

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

Select the graph of the function and determine whether it is even,odd,or neither.? $g ( t ) = \sqrt [ 3 ] { t - 4 }$ ?

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

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 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)

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

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.? $\left( - \frac { 1 } { 2 } , 5 \right)$ ?

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.? $\left( - \frac { 9 } { 7 } , - 4 \right)$ ?

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.

Select the graph of the function and determine whether it is even,odd,or neither. F(x) = |x + 6|

Quiz 5: Analyzing Graphs of Functions

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) ​

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) ​

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​ ?

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. ​

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. ​ (4,3) ​

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

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. ​

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. ​

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

Select the graph of the function and determine whether it is even,odd,or neither.? g(t) =t−43g ( t ) = \sqrt [ 3 ] { t - 4 }g(t) =3t−4​ ?

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

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 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) ​

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

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.? (−12,5) \left( - \frac { 1 } { 2 } , 5 \right) (−21​,5) ?

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.? (−97,−4) \left( - \frac { 9 } { 7 } , - 4 \right) (−79​,−4) ?

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. ​

Select the graph of the function and determine whether it is even,odd,or neither. ​ F(x) = |x + 6| ​

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)

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)

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

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.

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. (4,3)

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

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.

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.

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

Select the graph of the function and determine whether it is even,odd,or neither.? $g ( t ) = \sqrt [ 3 ] { t - 4 }$ ?

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

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 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)

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

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.? $\left( - \frac { 1 } { 2 } , 5 \right)$ ?

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.? $\left( - \frac { 9 } { 7 } , - 4 \right)$ ?

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.

Select the graph of the function and determine whether it is even,odd,or neither. F(x) = |x + 6|