Exam 4: Functions Functions and Function Notation

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation: $s = 192 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

(Multiple Choice)

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Question 41

Graph the function. $y = [ [ 2 x ] ]$

(Multiple Choice)

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Question 42

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$ . Find $f ^ { - 1 } ( x )$ .

(Multiple Choice)

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Question 43

Find the inverse of the one-to-one function. $y = 2 x + 7$

(Multiple Choice)

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Question 44

Find the inverse of the one-to-one function. $y = 8 x$

(Multiple Choice)

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Question 45

Graph the rational function. $f ( x ) = \frac { 5 x ^ { 3 } + 4 x } { 2 x }$ Note that the numerator and denominator of the fraction share a common factor.

(Multiple Choice)

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Question 46

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$ .

(Multiple Choice)

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Question 47

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function. $( g \circ g ) ( x )$

(Multiple Choice)

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Question 48

The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$ . Find $f ^ { - 1 } ( x )$ .

(Multiple Choice)

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Question 49

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 1 ) ^ { 3 } - 2$

(Multiple Choice)

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Question 50

Determine whether the function is one-to-one. $y = \frac { 4 } { 7 } x$

(Multiple Choice)

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Question 51

Find the inverse of the one-to-one function. $y = 7 x$

(Multiple Choice)

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Question 52

Graph the rational function. $f ( x ) = \frac { 3 x ^ { 3 } + 2 x } { 5 x }$ Note that the numerator and denominator of the fraction share a common factor.

(Multiple Choice)

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Question 53

A pizzeria charges $8.50 plus $0.90 per topping for a large pizza.Find the cost of a pizza that has 5 toppings.

(Multiple Choice)

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Question 54

A pizzeria charges $\$ 6.00$ plus $\$ 0.65$ per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

(Multiple Choice)

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Question 55

Find the vertex of the parabola. $y = 3 x ^ { 2 } - 2$

(Multiple Choice)

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Question 56

Find the vertex of the parabola. $y = 2 x ^ { 2 } - 8$

(Multiple Choice)

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Question 57

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 4 x + 5$

(Multiple Choice)

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Question 58

Graph the function. $f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$

(Multiple Choice)

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Question 59

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function. $( f - g ) ( x )$

(Multiple Choice)

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Question 60

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation: $s = 192 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

Graph the function. $y = [ [ 2 x ] ]$

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$ . Find $f ^ { - 1 } ( x )$ .

Find the inverse of the one-to-one function. $y = 2 x + 7$

Find the inverse of the one-to-one function. $y = 8 x$

Graph the rational function. $f ( x ) = \frac { 5 x ^ { 3 } + 4 x } { 2 x }$ Note that the numerator and denominator of the fraction share a common factor.

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$ .

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function. $( g \circ g ) ( x )$

The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$ . Find $f ^ { - 1 } ( x )$ .

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 1 ) ^ { 3 } - 2$

Determine whether the function is one-to-one. $y = \frac { 4 } { 7 } x$

Find the inverse of the one-to-one function. $y = 7 x$

Graph the rational function. $f ( x ) = \frac { 3 x ^ { 3 } + 2 x } { 5 x }$ Note that the numerator and denominator of the fraction share a common factor.

A pizzeria charges $8.50 plus $0.90 per topping for a large pizza.Find the cost of a pizza that has 5 toppings.

A pizzeria charges $\$ 6.00$ plus $\$ 0.65$ per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

Find the vertex of the parabola. $y = 3 x ^ { 2 } - 2$

Find the vertex of the parabola. $y = 2 x ^ { 2 } - 8$

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 4 x + 5$

Graph the function. $f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function. $( f - g ) ( x )$

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

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Natural Number Functions and Probability

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Exam 4: Functions Functions and Function Notation

At a time ttt seconds after an object is tossed vertically upward, it reaches a height sss in feet given by the equation: s=192t−16t2s = 192 t - 16 t ^ { 2 }s=192t−16t2 In how many seconds does the object reach its maximum height?

Graph the function. y=[[2x]]y = [ [ 2 x ] ]y=[[2x]]

The function f(x)=x2−6f ( x ) = \sqrt { x ^ { 2 } - 6 }f(x)=x2−6​ is one-to-one on the domain x≤−6x \leq - \sqrt { 6 }x≤−6​ . Find f−1(x)f ^ { - 1 } ( x )f−1(x) .

Find the inverse of the one-to-one function. y=2x+7y = 2 x + 7y=2x+7

Find the inverse of the one-to-one function. y=8xy = 8 xy=8x

Graph the rational function. f(x)=5x3+4x2xf ( x ) = \frac { 5 x ^ { 3 } + 4 x } { 2 x }f(x)=2x5x3+4x​ Note that the numerator and denominator of the fraction share a common factor.

The amount AAA of money on deposit for ttt years in an account earning simple interest is a linear function of ttt . Express that function as an equation if A=$28A = \$ 28A=$28 when t=1t = 1t=1 and A=$30A = \$ 30A=$30 when t=2t = 2t=2 .

Let f(x)=3x,g(x)=x+1f ( x ) = 3 x , g ( x ) = x + 1f(x)=3x,g(x)=x+1 . Find the composite function. (g∘g)(x)( g \circ g ) ( x )(g∘g)(x)

The function f(x)=x2−9f ( x ) = \sqrt { x ^ { 2 } - 9 }f(x)=x2−9​ is one-to-one on the domain x≤−9x \leq - \sqrt { 9 }x≤−9​ . Find f−1(x)f ^ { - 1 } ( x )f−1(x) .

The graph of the function g(x)g ( x )g(x) is a translation of the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . Graph the function. g(x)=(x−1)3−2g ( x ) = ( x - 1 ) ^ { 3 } - 2g(x)=(x−1)3−2

Determine whether the function is one-to-one. y=47xy = \frac { 4 } { 7 } xy=74​x

Find the inverse of the one-to-one function. y=7xy = 7 xy=7x

Graph the rational function. f(x)=3x3+2x5xf ( x ) = \frac { 3 x ^ { 3 } + 2 x } { 5 x }f(x)=5x3x3+2x​ Note that the numerator and denominator of the fraction share a common factor.

A pizzeria charges $8.50 plus $0.90 per topping for a large pizza.Find the cost of a pizza that has 5 toppings.

A pizzeria charges $6.00\$ 6.00$6.00 plus $0.65\$ 0.65$0.65 per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

Find the vertex of the parabola. y=3x2−2y = 3 x ^ { 2 } - 2y=3x2−2

Find the vertex of the parabola. y=2x2−8y = 2 x ^ { 2 } - 8y=2x2−8

Graph the quadratic function. f(x)=−x2−4x+5f ( x ) = - x ^ { 2 } - 4 x + 5f(x)=−x2−4x+5

Graph the function. f(x)=x2−2x−3x2−3x+5f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }f(x)=x2−3x+5x2−2x−3​

Let f(x)=2x−1,g(x)=3x−2f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2f(x)=2x−1,g(x)=3x−2 . Find the domain of the function. (f−g)(x)( f - g ) ( x )(f−g)(x)

A Review of Basic Algebra

Equations and Inequalities

The Rectangular Coordinate System and Graphs of Equations

Exponential and Logarithmic Functions

Solving Polynomial Equations

Linear Systems

Conic Sections and Quadratic Systems

Natural Number Functions and Probability

Filters

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation: $s = 192 t - 16 t ^ { 2 }$ In how many seconds does the object reach its maximum height?

Graph the function. $y = [ [ 2 x ] ]$

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$ . Find $f ^ { - 1 } ( x )$ .

Find the inverse of the one-to-one function. $y = 2 x + 7$

Find the inverse of the one-to-one function. $y = 8 x$

Graph the rational function. $f ( x ) = \frac { 5 x ^ { 3 } + 4 x } { 2 x }$ Note that the numerator and denominator of the fraction share a common factor.

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$ .

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function. $( g \circ g ) ( x )$

The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$ . Find $f ^ { - 1 } ( x )$ .

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 1 ) ^ { 3 } - 2$

Determine whether the function is one-to-one. $y = \frac { 4 } { 7 } x$

Find the inverse of the one-to-one function. $y = 7 x$

Graph the rational function. $f ( x ) = \frac { 3 x ^ { 3 } + 2 x } { 5 x }$ Note that the numerator and denominator of the fraction share a common factor.

A pizzeria charges $\$ 6.00$ plus $\$ 0.65$ per topping for a large pizza. Find the cost of a pizza that has 2 toppings.

Find the vertex of the parabola. $y = 3 x ^ { 2 } - 2$

Find the vertex of the parabola. $y = 2 x ^ { 2 } - 8$

Graph the quadratic function. $f ( x ) = - x ^ { 2 } - 4 x + 5$

Graph the function. $f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function. $( f - g ) ( x )$