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Common Core Standard HSF-IF.B.4 Questions

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★

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Grade 10 Functions and Relations CCSS: HSF-IF.B.4
For the absolute value function shown below, where is the function decreasing? Assume 1 unit intervals for both axes.
Graph - Absolute Function y=|1/2x|
  1. The function is never decreasing.
  2. For all values of x.
  3. [math]x>0[/math]
  4. [math]x<0[/math]
Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.B.4
Find the axis of symmetry of [math]f(x)=-1/2x^2+2x+5[/math].
Grade 10 Functions and Relations CCSS: HSF-IF.B.4
What is the inverse of the function [math]f(x) = x^3[/math]?
  1. [math]f^-1(x) = ∛x[/math]
  2. [math] f^-1(x) = ∛(x - 1)[/math]
  3. [math]f^-1(x) = x^(1/3)[/math]
  4. [math]f^-1(x) = x^(3/2)[/math]
Grade 10 Functions and Relations CCSS: HSF-IF.B.4
What is the inverse of the function [math]f(x) = 3x + 4[/math]?
  1. [math] f^-1(x) = (x - 4)/3[/math]
  2. [math]f^-1(x) = (x + 4)/3[/math]
  3. [math]f^-1(x) = 3x - 4[/math]
  4. [math]f^-1(x) = 3x + 4[/math]
Grade 10 Functions and Relations CCSS: HSF-IF.B.4
What is the inverse of the function [math]f(x) = 6 - 2x[/math]?
  1. [math]f^-1(x) = (6 - x)/2[/math]
  2. [math]f^-1(x) = (x - 6)/2[/math]
  3. [math]f^-1(x) = 2x - 6[/math]
  4. [math]f^-1(x) = 2x + 6[/math]
Grade 11 Function and Algebra Concepts CCSS: HSF-IF.B.4
What is the equation for the inverse of the function [math]f(x) = 2x + 3[/math]?
  1. [math]f^-1(x) = (x - 3)/2[/math]
  2. [math]f^-1(x) = 2/x + 3[/math]
  3. [math]f^-1(x) = -(x - 3)/2[/math]
  4. [math]f^-1(x) = (3 - x)/2[/math]
Grade 11 Function and Algebra Concepts CCSS: HSF-IF.B.4
What is the inverse of the function [math]f(x) = x^(-2)[/math]?
  1. [math]f^-1(x) = x^(-1/2)[/math]
  2. [math]f^-1(x) = -x^(-2)[/math]
  3. [math]f^-1(x) = x^2[/math]
  4. [math]f^-1(x) = -x^2[/math]
Grade 11 Function and Algebra Concepts CCSS: HSF-IF.B.4
What is a piecewise function?
  1. A function that is defined by multiple equations over different intervals
  2. A function that is defined by a single equation over the entire domain
  3. A function that is defined by a square root
  4. A function that is defined by a logarithm
Grade 11 Function and Algebra Concepts CCSS: HSF-IF.B.4
What is a horizontal line test used for?
  1. To determine if a relation is a function
  2. To determine if a graph is a parabola
  3. To determine if a graph is a straight line
  4. To determine if a graph is a circle
Grade 10 Quadratic Equations and Expressions CCSS: HSF-IF.B.4
Find the axis of symmetry of [math]f(x)=x^2+8x+21[/math].
Grade 11 Functions and Relations CCSS: HSF-IF.B.4
What is the equation of the line that passes through the point (3, 4) and is parallel to the line y = -2x + 5?
  1. y = -2x + 7
  2. y = -2x + 3
  3. y = 2x - 1
  4. y = -2x + 1
Grade 10 Functions and Relations CCSS: HSF-IF.B.4
Which of the following functions is one-to-one?
  1. [math]f(x) = x^2[/math]
  2. [math]f(x) = x^3[/math]
  3. [math]f(x) = √x[/math]
  4. [math]f(x) = |x|[/math]
Grade 10 Functions and Relations CCSS: HSF-IF.B.4
Which of the following functions has an inverse that is not a function?
  1. [math]f(x) = x^2[/math]
  2. [math]f(x) = x/2[/math]
  3. [math]f(x) = e^x[/math]
  4. [math]f(x) = |x|[/math]
Grade 10 Functions and Relations CCSS: HSF-IF.B.4
What is the inverse of the function [math]f(x) = 4x - 3[/math]?
  1. [math]f^-1(x) = (x + 3)/4[/math]
  2. [math]f^-1(x) = (x - 3)/4[/math]
  3. [math]f^-1(x) = 4x + 3[/math]
  4. [math]f^-1(x) = 4x - 3[/math]
Grade 11 Function and Algebra Concepts CCSS: HSF-IF.B.4
What is the inverse of the function [math]f(x) = x^2 + 1[/math]?
  1. [math]f^-1(x) = x^2 - 1[/math]
  2. [math]f^-1(x) = -x^2 + 1[/math]
  3. [math]f^-1(x) = sqrt(x + 1)[/math]
  4. [math]f^-1(x) = sqrt(x - 1)[/math]
Grade 11 Function and Algebra Concepts CCSS: HSF-IF.B.4
What is the main purpose of interpreting a function?
  1. To find the inverse of the function
  2. To understand the relationship between inputs and outputs
  3. To find the minimum or maximum value of the function
  4. To graph the function
Grade 11 Function and Algebra Concepts CCSS: HSF-IF.B.4
What is a step function?
  1. A function that jumps abruptly from one value to another at specific points
  2. A function that decreases continuously from one value to another over a specific interval
  3. A function that increases continuously from one value to another over a specific interval
  4. A function that is constant over a specific interval
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