Common Core Standard HSF-IF.C.7b Questions

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Grade 11 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

Graph the following piecewise function.

$f(x) = { {:(-3",", \ \ x<-2), (0",", \ \ -2<=x<=1), (3",", \ \ x>1):}$

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

What is the inverse of the function

$f(x) = x^2 + 4x + 5$ ?

$f^-1(x) = √(x - 5) - 2$
$f^-1(x) = -2x + √(x - 1)$
$f^-1(x) = √(x - 1) - 2$
$f^-1(x) = -2x + √(x - 5)$

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

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

$g(x) = x - 2$ , what is the composition

$(f o g)(x)$ ?

$2x^3 - 4x^2 - 3x - 6$
$2x^3 - 7x + 3$
$2x^2 - 7x + 3$
$2x^2 + 7x - 3$

Grade 10 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

When graphing a square root function of the form

$f(x) = a sqrt(bx + c) +d$ , where

$a,b,c,d in RR$ , there is always either a minimum or maximum value (but not both).

True
False

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following is the domain of the function

$f(x) = (x - 2)/(x + 1)$ ?

All real numbers
All real numbers except $x = 1$
All real numbers except $x = -1$
All real numbers except $x = -2$

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following is the inverse function of

$f(x) = 2x + 1$ ?

$f(x) = 2x - 1$
$f(x) = (x - 1)/2$
$f(x) = (x + 1)/2$
$f(x) = (x - 1)/2 + 1$

Grade 10 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

When graphing a cube root function of the form

$f(x) = a root[3](x+b) + c$ , where

$a,b,c in RR$ , the range is all real numbers.

True
False

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

What is the range of the function

$f(x) = 2x^2 - 4x + 3$ ?

All real numbers
All real numbers greater than or equal to 3
All real numbers greater than or equal to $-3/2$
All real numbers greater than or equal to $-1/2$

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following is equivalent to

$(f o g)(x)$ ?

$f(g(x))$
$g(f(x))$
$f(x)g(x)$
$f(x) + g(x)$

Grade 10 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

When graphing a square root function of the form

$f(x) = a sqrt(bx+c) + d$ , where

$a,b,c,d in RR$ , there will never be any part of the graph to the left of the y-axis.

True
False

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following statements about inverse functions is true?

Every function has an inverse.
Every inverse function is also a function.
The graph of a function and its inverse are always mirror images of each other.
The composition of a function and its inverse is the identity function.

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

$f(x) = x^2 - 1$ and

$g(x) = 3x + 2$ , what is

$f(g(-1))$ ?

0
-2
8
10

Grade 10 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

Graph the square root function

$f(x) = 2sqrt(x) + 1$ .

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following is the inverse of the function

$f(x) = 2x + 1$ ?

$f^-1(x) = (x - 1)/2$
$f^-1(x) = (x + 1)/2$
$f^-1(x) = 2x - 1$
$f^-1(x) = 2(x - 1)$

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following functions is one-to-one?

$f(x) = x^2 + 4x + 4$
$f(x) = 2x - 1$
$f(x) = sin(x)$
$f(x) = e^x$

Grade 10 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

Graph the function

$f(x) = -3sqrt(x - 2)$ .

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

What is the inverse of the function

$f(x) = √(x + 4)$ ?

$f^-1(x) = x^2 - 4$
$f^-1(x) = x^2 + 4$
$f^-1(x) = x^2 - 16$
$f^-1(x) = x^2 + 16$

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following statements is true about the graphs of inverse functions?

The graphs of inverse functions are always linear.
The graphs of inverse functions are always symmetric with respect to the x-axis.
The graphs of inverse functions are reflections of each other across the line y = x.
The graphs of inverse functions intersect at exactly one point.

Grade 11 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

Graph the function

$f(x) = 2root[3](x) - 4$ .

Grade 11 Functions and Relations CCSS: HSF-IF.C.7b

Which of the following is the domain of the function

$f(x) = 1/(x - 2)$ ?

All real numbers
All real numbers except $x = 2$
All real numbers except $x = -2$
All real numbers except $x = 1/2$

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Common Core Standard HSF-IF.C.7b Questions

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