Question 1

Determine whether the equation defines y as a function of x.
-$y=\frac{1}{x}$

A) function
B) not a function

Accepted Answer

For every value of x (except x = 0, where the expression is undefined), there is exactly one corresponding value of y. This satisfies the definition of a function.

Question 2

Determine whether the equation defines y as a function of x.
-$x+7 y=5$

A) function
B) not a function

Accepted Answer

The equation $x + 7y = 5$ can be rearranged to solve for $y$ in terms of $x$, which is $y = \frac{5 - x}{7}$. This shows that for every value of $x$, there is exactly one corresponding value of $y$, which meets the definition of a function.

Question 3

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$\{(-1,-3),(-2,-2),(-2,0),(2,2),(14,4)\}$

A) function
domain: $ \{-3,-2,0,2,4\} $
range: $ \{-1,2,-2,14\} $

B) function
domain: $ \{-1,2,-2,14\} $
range: $ \{-3,-2,0,2,4\} $

C) $\text { not a function }$

Accepted Answer

A relation is a function if each input (x-value) has exactly one output (y-value). In this relation, the input -2 is associated with two different outputs (-2 and 0), so it is not a function.

Question 4

Determine whether the equation defines y as a function of x.
-$y=|x|$

A) function
B) not a function

Accepted Answer

The equation $y=|x|$ defines y as a function of x because for every value of x, there is exactly one corresponding value of y. The absolute value ensures that y is non-negative, but does not create multiple y values for any single x value.

Question 5

Determine whether the equation defines y as a function of x.
-$y=\pm \sqrt{1-5 x}$

A) function
B) not a function

Accepted Answer

The equation $y=\pm \sqrt{1-5 x}$ does not define y as a function of x because for each x in the domain, there are two possible y values (one positive and one negative), violating the definition of a function which requires each input to have exactly one output.

Question 6

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$\begin{aligned}
4 & \rightarrow 8 \
9 & \rightarrow 18 \
14 & \rightarrow 28 \
19 & \rightarrow 38
\end{aligned}$

A) function
domain: $ \{8,18,28,38\} $
range: $ \{4,9,14,19\} $

B) function
domain: $ \{4,9,14,19\} $
range: $ \{8,18,28,38\} $

C) $\text { not a function }$

Accepted Answer

Each input (4, 9, 14, 19) is associated with exactly one output (8, 18, 28, 38), which defines a function. The domain is the set of inputs $\{4,9,14,19\}$, and the range is the set of outputs $\{8,18,28,38\}$.

Question 7

Determine whether the equation defines y as a function of x.
-$x=y^{2}$

A) function
B) not a function

Accepted Answer

The equation $x=y^{2}$ does not define y as a function of x because for a given x-value, there can be two different y-values (one positive and one negative), violating the definition of a function where each input must have exactly one output.

Question 8

Determine whether the equation defines y as a function of x.
-$y=7 x^{2}-2 x+8$

A) function
B) not a function

Accepted Answer

The equation $y=7x^2-2x+8$ defines y as a function of x because for each value of x, there is exactly one corresponding value of y. This satisfies the definition of a function.

Question 9

Determine whether the equation defines y as a function of x.
-$-4 x+x^{2}-58=y$

A) function
B) not a function

Accepted Answer

For any given value of x, there is exactly one corresponding value of y, satisfying the definition of a function.

Question 10

Determine whether the equation defines y as a function of x.
-$y=\frac{5 x+3}{x+2}$

A) function
B) not a function

Accepted Answer

The equation $y=\frac{5x+3}{x+2}$ defines y as a function of x because for each value of x (except $x \neq -2$ to avoid division by zero), there is exactly one corresponding value of y. This satisfies the definition of a function.

Question 11

Determine whether the equation defines y as a function of x.
-$x^{2}=8-x^{2}$

A) function
B) not a function

Accepted Answer

The equation does not define y as a function of x because it does not involve y. It is simply an equation in terms of x, and when solved, it does not result in a relationship where for each x there is a unique y.

Question 12

Determine whether the relation represents a function. If it is a function, state the domain and range.
-

A)
function
$\text { domain: \{carrots, peas, squash }$
$\text { range: \{Bob. Ann. Dave\} }$

B)
function
$\text { domain: \{Bob, Ann, Dave\} }$
$\text { range: \{carrots, peas, squash\} }$

C)
$\text { not a function }$

Accepted Answer

The answer of Determine whether the relation represents a function....

Question 13

Determine whether the relation represents a function. If it is a function, state the domain and range.
-

A) function
domain: {Ms. Lee, Mr. Bar}
range: $ \{ $ Bob, Ann, Dave $ \} $

B) function
domain: {Bob, Ann, Dave}
range:{Ms. Lee, Mr. Bar}

C) $\text { not a function }$

Accepted Answer

The answer of Determine whether the relation represents a function....

Question 14

Determine whether the equation defines y as a function of x.
-$x^{2}+2 y^{2}=1$

A) function
B) not a function

Accepted Answer

The equation $x^{2}+2y^{2}=1$ does not define y as a function of x because for a given x-value, there can be two different y-values (one positive and one negative) that satisfy the equation, violating the definition of a function where each input should have exactly one output.

Question 15

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$\{(-4,11),(-3,4),(0,-5),(3,4),(5,20)\}$

A) function
domain: $ \{11,4,-5,20\} $
range: $ \{-4,-3,0,3,5\} $

B) function
domain: $ \{-4,-3,0,3,5\} $
range: $ \{11,4,-5,20\} $

C) $\text { not a function }$

Accepted Answer

A relation is a function if each input (x-value) has exactly one output (y-value). In this relation, each x-value is paired with exactly one y-value, so it is a function. The domain (all the x-values) is $\{-4,-3,0,3,5\}$, and the range (all the y-values) is $\{11,4,-5,20\}$.

Question 16

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$(-3,6),(2,3),(3,-3),(8,-1)$
A) function
domain: $ \{6,3,-3,-1\} $
range: $ \{-3,2,3,8\} $

B) function
domain: $ \{-3,2,3,8\} $
range: $ \{6,3,-3,-1\} $

C) $\text { not a function }$

Accepted Answer

A relation is a function if each input (x-value) has exactly one output (y-value). The given relation has unique x-values for each pair, making it a function. The domain (x-values) is $\{-3,2,3,8\}$, and the range (y-values) is $\{6,3,-3,-1\}$.

Question 17

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$\left\{(2.44,3.24),(2.444,-3.2),\left(\frac{7}{3}, 0\right),(2.33,-2)\right\}$

A) function
domain: $ \{3.24,-3.2,0,-2\} $
range: $ \left\{2.44,2.444, \frac{7}{3}, 2.33\right\} $

B) function
domain: $ \left\{2.44,2.444, \frac{7}{3}, 2.33\right\} $
range: $ \{3.24,-3.2,0,-2\} $

C) $\text { not a function }$

Accepted Answer

A relation is a function if each input (x-value) has exactly one output (y-value). In this relation, each x-value is unique and paired with exactly one y-value, making it a function. The domain is the set of all x-values, and the range is the set of all y-values.

Question 18

Find the value for the function.
-$\text { Find } f(4) \text { when } f(x)=x^{2}-4 x+3$

A) -3
B) 35
C) 3
D) 29

Accepted Answer

The answer of Find the value for the function.
-\(\text {...

Question 19

Determine whether the equation defines y as a function of x.
-$y=x^{4}$

A) function
B) not a function

Accepted Answer

The equation $y = x^{4}$ defines y as a function of x because for each value of x, there is exactly one corresponding value of y. This satisfies the definition of a function.

Question 20

Determine whether the equation defines y as a function of x.
-$y^{2}+x=2$

A) function
B) not a function

Accepted Answer

For an equation to define y as a function of x, each value of x must correspond to exactly one value of y. The given equation $y^{2}+x=2$ can be rewritten as $y^{2}=2-x$, which implies that for any given value of x (except when $2-x<0$), there are two possible values of y (one positive and one negative square root of $2-x$). Therefore, it does not define y as a function of x.

Quiz 1: Functions and Their Graphs

Determine whether the equation defines y as a function of x. - $y=\frac{1}{x}$

Determine whether the equation defines y as a function of x. - $x+7 y=5$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{(-1,-3) ,(-2,-2) ,(-2,0) ,(2,2) ,(14,4) \}$

Determine whether the equation defines y as a function of x. - $y=|x|$

Determine whether the equation defines y as a function of x. - $y=\pm \sqrt{1-5 x}$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\begin{aligned}4 & \rightarrow 8 \\9 & \rightarrow 18 \\14 & \rightarrow 28 \\19 & \rightarrow 38\end{aligned}$

Determine whether the equation defines y as a function of x. - $x=y^{2}$

Determine whether the equation defines y as a function of x. - $y=7 x^{2}-2 x+8$

Determine whether the equation defines y as a function of x. - $-4 x+x^{2}-58=y$

Determine whether the equation defines y as a function of x. - $y=\frac{5 x+3}{x+2}$

Determine whether the equation defines y as a function of x. - $x^{2}=8-x^{2}$

Determine whether the equation defines y as a function of x. - $x^{2}+2 y^{2}=1$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{(-4,11) ,(-3,4) ,(0,-5) ,(3,4) ,(5,20) \}$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $(-3,6) ,(2,3) ,(3,-3) ,(8,-1)$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\left\{(2.44,3.24) ,(2.444,-3.2) ,\left(\frac{7}{3}, 0\right) ,(2.33,-2) \right\}$

Find the value for the function. - $\text { Find } f(4) \text { when } f(x) =x^{2}-4 x+3$

Determine whether the equation defines y as a function of x. - $y=x^{4}$

Determine whether the equation defines y as a function of x. - $y^{2}+x=2$

Quiz 1: Functions and Their Graphs

Determine whether the equation defines y as a function of x. - y=1xy=\frac{1}{x}y=x1​

Determine whether the equation defines y as a function of x. - x+7y=5x+7 y=5x+7y=5

Determine whether the relation represents a function. If it is a function, state the domain and range. - {(−1,−3) ,(−2,−2) ,(−2,0) ,(2,2) ,(14,4) }\{(-1,-3) ,(-2,-2) ,(-2,0) ,(2,2) ,(14,4) \}{(−1,−3) ,(−2,−2) ,(−2,0) ,(2,2) ,(14,4) }

Determine whether the equation defines y as a function of x. - y=∣x∣y=|x|y=∣x∣

Determine whether the equation defines y as a function of x. - y=±1−5xy=\pm \sqrt{1-5 x}y=±1−5x​

Determine whether the relation represents a function. If it is a function, state the domain and range. - 4→89→1814→2819→38\begin{aligned}4 & \rightarrow 8 \\9 & \rightarrow 18 \\14 & \rightarrow 28 \\19 & \rightarrow 38\end{aligned}491419​→8→18→28→38​

Determine whether the equation defines y as a function of x. - x=y2x=y^{2}x=y2

Determine whether the equation defines y as a function of x. - y=7x2−2x+8y=7 x^{2}-2 x+8y=7x2−2x+8

Determine whether the equation defines y as a function of x. - −4x+x2−58=y-4 x+x^{2}-58=y−4x+x2−58=y

Determine whether the equation defines y as a function of x. - y=5x+3x+2y=\frac{5 x+3}{x+2}y=x+25x+3​

Determine whether the equation defines y as a function of x. - x2=8−x2x^{2}=8-x^{2}x2=8−x2

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Determine whether the equation defines y as a function of x. - x2+2y2=1x^{2}+2 y^{2}=1x2+2y2=1

Determine whether the relation represents a function. If it is a function, state the domain and range. - {(−4,11) ,(−3,4) ,(0,−5) ,(3,4) ,(5,20) }\{(-4,11) ,(-3,4) ,(0,-5) ,(3,4) ,(5,20) \}{(−4,11) ,(−3,4) ,(0,−5) ,(3,4) ,(5,20) }

Determine whether the relation represents a function. If it is a function, state the domain and range. - (−3,6) ,(2,3) ,(3,−3) ,(8,−1) (-3,6) ,(2,3) ,(3,-3) ,(8,-1) (−3,6) ,(2,3) ,(3,−3) ,(8,−1)

Determine whether the relation represents a function. If it is a function, state the domain and range. - {(2.44,3.24) ,(2.444,−3.2) ,(73,0) ,(2.33,−2) }\left\{(2.44,3.24) ,(2.444,-3.2) ,\left(\frac{7}{3}, 0\right) ,(2.33,-2) \right\}{(2.44,3.24) ,(2.444,−3.2) ,(37​,0) ,(2.33,−2) }

Find the value for the function. - Find f(4) when f(x) =x2−4x+3\text { Find } f(4) \text { when } f(x) =x^{2}-4 x+3 Find f(4) when f(x) =x2−4x+3

Determine whether the equation defines y as a function of x. - y=x4y=x^{4}y=x4

Determine whether the equation defines y as a function of x. - y2+x=2y^{2}+x=2y2+x=2

Determine whether the equation defines y as a function of x. - $y=\frac{1}{x}$

Determine whether the equation defines y as a function of x. - $x+7 y=5$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{(-1,-3) ,(-2,-2) ,(-2,0) ,(2,2) ,(14,4) \}$

Determine whether the equation defines y as a function of x. - $y=|x|$

Determine whether the equation defines y as a function of x. - $y=\pm \sqrt{1-5 x}$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\begin{aligned}4 & \rightarrow 8 \\9 & \rightarrow 18 \\14 & \rightarrow 28 \\19 & \rightarrow 38\end{aligned}$

Determine whether the equation defines y as a function of x. - $x=y^{2}$

Determine whether the equation defines y as a function of x. - $y=7 x^{2}-2 x+8$

Determine whether the equation defines y as a function of x. - $-4 x+x^{2}-58=y$

Determine whether the equation defines y as a function of x. - $y=\frac{5 x+3}{x+2}$

Determine whether the equation defines y as a function of x. - $x^{2}=8-x^{2}$

Determine whether the equation defines y as a function of x. - $x^{2}+2 y^{2}=1$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{(-4,11) ,(-3,4) ,(0,-5) ,(3,4) ,(5,20) \}$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $(-3,6) ,(2,3) ,(3,-3) ,(8,-1)$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\left\{(2.44,3.24) ,(2.444,-3.2) ,\left(\frac{7}{3}, 0\right) ,(2.33,-2) \right\}$

Find the value for the function. - $\text { Find } f(4) \text { when } f(x) =x^{2}-4 x+3$

Determine whether the equation defines y as a function of x. - $y=x^{4}$

Determine whether the equation defines y as a function of x. - $y^{2}+x=2$