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Common Core Standard HSF-IF.A.1 Questions

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

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Grade 9 Functions and Relations CCSS: HSF-IF.A.1
Which relation represents a function?
  1. {(2,6), (-3,6), (4,9), (2,10)}
  2. {(-4,4), (-3, 3), (-2,2), (-1,1), (-4, 0)}
  3. {(3,5), (4, 8), (2, 9)}
  4. {(8, 0), (5,2), (8,-1), (4,-2)}
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
Which of the following states the range for the function [math]h(x) = cos(x) + 1 ?[/math]
  1. [math][0,2][/math]
  2. [math][-1,1][/math]
  3. [math](-oo,oo)[/math]
  4. [math][-2,2][/math]
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
State the domain: [math]f(x)= (-1)/(x-5)[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
Is the following graph a function?
Graph - Absolute Function y=|x|
  1. Yes
  2. No
Grade 10 Functions and Relations CCSS: HSF-IF.A.1
Where is the output of the function graphed below less than 2? Assume the horizontal axis represents [math]x[/math] and the vertical axis represents [math]y[/math].
Graph - Quadratic Function y=1/2x^2
  1. [math]x<2[/math]
  2. [math]-2 < y < 2[/math]
  3. [math]-2 < x < 2[/math]
  4. [math]y<2[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
Let [math]g(x) = sqrt(x^2-4)[/math]. What is the domain of [math]g(x) ?[/math]
  1. [math](-oo,oo)[/math]
  2. [math](-oo,-2] uu [2,oo)[/math]
  3. [math][-2,2][/math]
  4. [math][2,oo)[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
What is the equation of the line that passes through the points (1, 2) and (3, 5)?
  1. y = 3x - 1
  2. y = 2x + 1
  3. y = x + 2
  4. y = 4x - 3
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
The domain is {-2, -2, 0, 1, 5} and the range is {-2, 0, 1, -2, 5}.

The given domain and range determines that the sets of numbers are
  1. a function, and linear.
  2. not a function, but linear.
  3. a function, but not linear.
  4. not a function, and not linear.
Grade 11 Functions and Relations CCSS: HSF-IF.A.1, HSF-BF.A.1, HSF-BF.A.1c
Find the domain of the composite function [math]f(g(x))[/math].

[math]f(x)= x+3[/math]
[math]g(x)= 2/(x+6)[/math]
  1. [math](-oo,3) uu (3,oo)[/math]
  2. [math](-oo,oo)[/math]
  3. [math](-oo,-6) uu (-6,3) uu (3,oo)[/math]
  4. [math](-oo,-6) uu (-6,oo)[/math]
Grade 10 Functions and Relations CCSS: HSF-IF.A.1
Is the following a function? Explain why or why not.
Coordinate Plane - 5x5 - With Dots
  1. Yes, this does represent a function, because all the points are distinct (none of them are coincident).
  2. No, this does not represent a function, since a function can not be made up of only points.
  3. No, this does not represent a function, since it fails the vertical line test.
  4. No, this does not represent a function, since a function is made up of many more points.
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
What is the range of [math]f(x) = -3*2^(2x-5) ?[/math]
  1. [math](-3,oo)[/math]
  2. [math](0,oo)[/math]
  3. [math](-oo,oo)[/math]
  4. [math](-oo,0)[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
What is the equation of the line that is perpendicular to the line y = -3x + 4 and passes through the point (2,1)?
  1. y = 3x + 1
  2. y = -3x - 1
  3. y = 3x - 5
  4. y = -3x + 5
Grade 10 Functions and Relations CCSS: HSF-IF.A.1
Given the following for [math]y = f(x)[/math]:

[math]y in {1, 3, 5, 7, 9}[/math]
[math]x in {2, 4, 6, 8, 10} [/math]

What is true about the given?
  1. The range is the values of y.
  2. The domain is the set of all even integers.
  3. The range is the set of all odd integers.
  4. The domain and range include all real numbers.
Grade 11 Functions and Relations CCSS: HSF-IF.A.1
Determine which relation is a function.
  1. {(3,0), (0,3), (5,4), (0,1)}
  2. {(0,0), (0,3), (0,4), (0,1)}
  3. {(-1,0), (0,3), (-1,4), (5,2)}
  4. {(3,0), (2,3), (5,4), (6,1)}
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