What is the characteristic shape of the graph of the absolute value parent function, $f(x) = |x|$?

A V-shape with its vertex at the origin

A diagonal line with a slope of 1

Parent Functions and Transformations Practice — Grade 8 math

Lesson 1: Parent Functions and Transformations — Practice Questions

1. Which type of parent function is represented by the equation $f(x) = x^2$?
- A. Constant
- B. Linear
- C. Absolute Value
- D. Quadratic
2. What is the characteristic shape of the graph of the absolute value parent function, $f(x) = |x|$?
- A. A horizontal line
- B. A V-shape with its vertex at the origin
- C. A U-shaped parabola
- D. A diagonal line with a slope of 1
3. For the quadratic parent function $f(x) = x^2$, what is the value of $f(-5)$? ___
4. A constant function is defined by $f(x) = c$. If the graph of a constant function passes through the point $(2, 7)$, what is the value of $c$? ___
5. Which equation represents the linear parent function?
- A. $f(x) = 5$
- B. $f(x) = x$
- C. $f(x) = |x|$
- D. $f(x) = x^2$
6. How is the graph of $g(x) = (x + 2)^2$ transformed from the parent function $f(x) = x^2$?
- A. Shifted 2 units right
- B. Shifted 2 units left
- C. Shifted 2 units up
- D. Shifted 2 units down
7. The function $g(x) = |x| - 7$ is a translation of the parent function $f(x) = |x|$ down by ___ units.
8. Which term best describes the transformation of $f(x) = x^2$ to $g(x) = 4x^2$?
- A. Vertical stretch
- B. Vertical shrink
- C. Reflection across the x-axis
- D. Horizontal shift
9. Which set of transformations maps the graph of $f(x) = |x|$ to $g(x) = -|x - 5| + 1$?
- A. Reflect across x-axis, shift 5 units right, shift 1 unit up
- B. Reflect across x-axis, shift 5 units left, shift 1 unit up
- C. Reflect across y-axis, shift 5 units right, shift 1 unit down
- D. Shift 5 units left, shift 1 unit down