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Quizzes > High School Quizzes > Mathematics

Parent Functions Practice Quiz

Enhance your skills with interactive math challenges

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting Parent Function Frenzy, an engaging high school algebra quiz.

Which of the following is the parent function of y = x^2?
y = x^2
y = x
y = |x|
y = sqrt(x)
The function y = x^2 is the basic quadratic function and forms a parabola opening upward. It is the parent function for all quadratic functions.
What is the simplest form of a linear parent function?
y = x
y = x^2
y = |x|
y = sqrt(x)
The function y = x represents a straight line passing through the origin with a slope of 1. It is the parent function for all linear functions.
Which function is the parent function for absolute value functions?
y = |x|
y = x^2
y = x
y = sqrt(x)
The function y = |x| is the basic absolute value function, forming a distinctive V-shaped graph. It serves as the parent function for all absolute value transformations.
Identify the parent function for the square root function.
y = sqrt(x)
y = x^2
y = |x|
y = x
The function y = sqrt(x) is the simplest form of a square root function. Its graph starts at the origin and increases gradually to the right.
Which function represents the reciprocal parent function?
y = 1/x
y = x
y = x^2
y = |x|
y = 1/x is the foundational reciprocal function characterized by its hyperbolic shape and distinct asymptote at x = 0. This makes it easily recognizable among parent functions.
Given the function f(x) = x^2 + 6, what is its parent function?
y = x^2
y = x
y = |x|
y = sqrt(x)
The function f(x) = x^2 + 6 is a vertical shift of the quadratic parent function y = x^2. The constant added moves the graph upward while maintaining its parabolic shape.
What is the parent function of f(x) = |x - 3| - 2?
y = |x|
y = x^2
y = x
y = sqrt(x)
f(x) = |x - 3| - 2 is derived from the absolute value parent function y = |x|. The shifts applied do not alter its inherent V-shaped structure.
Which of the following functions is an example of an exponential parent function with a base greater than 1?
y = 2^x
y = x^2
y = log(x)
y = sqrt(x)
y = 2^x is the exponential parent function that grows rapidly as x increases. Its curve is distinctly different from those of polynomial or radical functions.
What is the parent function for f(x) = log(x)?
y = log(x)
y = 2^x
y = x^2
y = sqrt(x)
The function f(x) = log(x) is the basic logarithmic function and serves as its own parent function. It is known for its slow growth and is the inverse of the exponential function.
Which of the following functions is an example of a cubic parent function?
y = x^3
y = x^2
y = |x|
y = sqrt(x)
y = x^3 showcases the standard cubic shape with its characteristic S-curve and symmetry about the origin. It is universally accepted as the parent function for cubic functions.
Which parent function has a domain that excludes x = 0?
y = 1/x
y = x
y = x^2
y = |x|
The reciprocal function y = 1/x is undefined at x = 0, making its domain all real numbers except zero. This feature distinguishes it from most other parent functions which are defined for every real number.
If g(x) = log(x - 2) + 3, what is its parent function?
y = log(x)
y = 2^x
y = x^2
y = |x|
Although g(x) = log(x - 2) + 3 includes horizontal and vertical shifts, its inherent shape is that of the logarithmic parent function y = log(x). Shifts do not change the basic behavior of the function.
Consider the function h(x) = sqrt(x + 5) - 1. Which is its parent function?
y = sqrt(x)
y = x^2
y = log(x)
y = |x|
h(x) is a shifted version of the square root function. The horizontal and vertical adjustments do not alter the fundamental shape of the parent function y = sqrt(x).
The function f(x) = -x^2 is a transformation of which parent function?
y = x^2
y = |x|
y = x
y = 1/x
The negative sign in f(x) = -x^2 reflects the quadratic graph over the x-axis. Despite the reflection, the original shape derives from the quadratic parent function y = x^2.
Which parent function typically exhibits symmetry about the origin?
y = x^3
y = x^2
y = |x|
y = sqrt(x)
The cubic function y = x^3 is an odd function, meaning it is symmetric with respect to the origin. This characteristic sets it apart from even functions like y = x^2.
Which parent function is used in f(x) = 1/(x - 3) and what transformation does it undergo?
y = 1/x, shifted right by 3
y = 1/x, shifted left by 3
y = x, shifted right by 3
y = x, shifted left by 3
The function f(x) = 1/(x - 3) is a horizontal translation of the reciprocal parent function y = 1/x. The shift moves the vertical asymptote from x = 0 to x = 3.
What is the inverse of the exponential parent function f(x) = 2^x?
f❻¹(x) = log₂(x)
f❻¹(x) = 2^(1/x)
f❻¹(x) = x²
f❻¹(x) = √x
The inverse of an exponential function like 2^x is the corresponding logarithmic function with base 2, denoted as log₂(x). This inverse relationship is a fundamental concept in algebra.
A transformation of the cubic function f(x) = x^3 results in g(x) = (x + 2)^3 - 4. Which transformations are applied?
Shift left by 2 and down by 4
Shift right by 2 and up by 4
Shift left by 2 and up by 4
Shift right by 2 and down by 4
Replacing x with (x + 2) shifts the graph of x^3 two units to the left, and subtracting 4 shifts it downward by 4 units. These transformations reposition the graph without altering its cubic nature.
Which parent function and transformation produces f(x) = -√(x - 1)?
y = √x, reflected over the x-axis and shifted right by 1
y = √x, reflected over the y-axis and shifted left by 1
y = |x|, reflected over the x-axis and shifted right by 1
y = x^2, shifted right by 1 and reflected
f(x) = -√(x - 1) comes from the square root parent function y = √x. The (x - 1) indicates a rightward shift of 1 unit, and the negative sign reflects the graph across the x-axis.
Determine the transformation for f(x) = |x| - 3. What is the parent function and transformation?
y = |x|, shifted down by 3
y = |x|, shifted up by 3
y = x^2, shifted down by 3
y = x^2, shifted up by 3
f(x) = |x| - 3 is obtained by subtracting 3 from the absolute value function y = |x|, which shifts the graph downward. The base V-shaped graph remains unchanged aside from the vertical translation.
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Study Outcomes

  1. Identify key characteristics of common parent functions.
  2. Analyze the behavior of parent function graphs.
  3. Interpret transformations and shifts applied to parent functions.
  4. Compare and contrast differences between various parent functions.
  5. Apply knowledge of parent functions to solve algebraic problems.

Parent Functions Cheat Sheet

  1. Understand parent functions - Parent functions are the simplest version of a function family, acting like the "default settings" for more complex graphs. They give you a baseline shape before any shifts, stretches, or flips occur. Story of Mathematics
  2. Familiarize yourself with common types - There are ten classic parent functions you'll run into: constant, linear, quadratic, cubic, absolute value, square root, cube root, reciprocal, exponential, and logarithmic. Each one has its own signature curve that shows up again and again in algebra and calculus. ChiliMath
  3. Recognize basic transformations - Transformations include translations (shifts), reflections (flips), stretches, and compressions, all of which change a graph's position or shape. By mastering these moves, you can predict how any parent function will look after algebraic tweaks. MathHints
  4. Vertical shifts - Adding or subtracting a constant outside the function moves the graph up or down. For example, f(x)+3 shifts every point 3 units upward, while f(x) - 2 drops it 2 units lower. MathHints
  5. Horizontal shifts - Placing a constant inside the function, like f(x+4) or f(x - 5), pushes the graph left or right. Remember: f(x+4) moves left 4, and f(x - 5) moves right 5 - it's the opposite of what you might expect! MathHints
  6. Vertical stretches and compressions - Multiplying the entire function by a factor a (>1) makes it taller (a vertical stretch), while 0<a<1 squashes it toward the x-axis (vertical compression). It's like zooming in and out on the y-scale. MathHints
  7. Horizontal stretches and compressions - Multiplying the input x by a factor inside the function has the opposite effect on the x-axis: a>1 squeezes the graph inward, and 0<a<1 pulls it outward. Think of it as reshaping the curve left and right. MathHints
  8. Reflections across axes - Multiply the whole function by - 1 to flip it over the x-axis, or multiply x by - 1 inside the function to mirror it across the y-axis. These flips turn peaks into valleys and vice versa in a flash. MathHints
  9. Practice with real examples - Analyze graphs and equations side by side to spot which parent function you're dealing with and what happened to it. The more you play detective, the faster you'll tune into patterns and transformations. MathPlane
  10. Keep building your skills - Mastering parent functions and their transformations lays the groundwork for tackling advanced algebra and calculus topics. Stay curious, practice daily, and watch your confidence skyrocket! Story of Mathematics
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