Question 1

Which of the following is the correct equation for the parent function shown in the first image (a straight line passing through the origin at a 45-degree angle)?

Accepted Answer

$$f(x) = x$$

Question 2

What is the domain and range of the function $$f(x) = |x| as $$shown in the second image?

Accepted Answer

Domain: $$x \in \mathbb{R}$$, Range: $$y \geq 0$$

Question 3

Which transformation describes the function $$f(x) = (x-3)^2$ + 2$$ compared to the parent function $$f(x) = x^2$?

Accepted Answer

Shifted 3 units right and 2 units up

Question 4

Given the piecewise function:

$$ f(x) = \begin{cases} 2, & x  -2 \end{cases} $$

What is $$f(-4)$$?

Accepted Answer

$$2$$

Question 5

Which parent function is shown in the fourth image (starts at the origin and curves upward to the right)?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 6

A chemical reaction's rate is modeled by $$f(x) = \frac{1}{x}. $$What is the domain of this function?

Accepted Answer

$$x 
eq 0$$

Question 7

Which transformation will reflect the graph of $$f(x) = x^3$ over the x-axis?

Accepted Answer

$$f(x) = -x^3$

Question 8

A population of bacteria doubles every hour and is modeled by $$f(x) = 2^x. $$Which parent function does this represent?

Accepted Answer

$$f(x) = a^x$$

Question 9

Given the function $$f(x) = |x-4| + 2$$, what is the vertex of the graph?

Accepted Answer

$$(4, 2)$$

Question 10

Which of the following best describes the range of the function $$f(x) = x^2$?

Accepted Answer

$$y \geq 0$$

Question 11

A piecewise function is defined as $$f(x) = \begin{cases} -x^2$ + 18, & x \u003c -2 \ 2x + 1, & x \geq -2 \end{cases}. $$What is $$f(-4)$$?

Accepted Answer

$$-(-4)^2 + 18$

Question 12

Which parent function is shown in the sixth image (an S-shaped curve passing through the origin)?

Accepted Answer

$$f(x) = x^3$

Question 13

If $$f(x) = x^2$ and g(x) = f(x-3) + 2$, what is the effect of these transformations?

Accepted Answer

Shift right 3 units, up 2 units

Question 14

Which of the following is NOT a characteristic of the graph of $$f(x) = \frac{1}{x}$$?

Accepted Answer

It passes through the origin

Question 15

Given the function $$f(x) = -2|x+1| + 3$$, what is the vertex of the graph?

Accepted Answer

$$(-1, 3)$$

Question 16

Which transformation will stretch the graph of $$f(x) = x^2$ vertically by a factor of 3?

Accepted Answer

$$f(x) = 3x^2$

Question 17

A medical dosage is modeled by $$f(x) = \sqrt{x-2}. $$What is the domain of this function?

Accepted Answer

$$x \geq 2$$

Question 18

Which parent function is shown in the seventh image (an S-shaped curve, but less steep than $$x^3$$)?

Accepted Answer

$$f(x) = \sqrt[3]{x}$$

Question 19

If $$f(x) = x^2$ and g(x) = -f(x$$)$$, what is the effect of this transformation?

Accepted Answer

Reflection over the x-axis

Parent Functions, Transformations, and Piecewise Functions in College Algebra

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