Functions

Determining if Linear

Determine if the function

f (x) = 3 x + 5

is linear.

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Rewriting as an Equation

If the function

f (x) = 2 x + 3

, find the equation of the function when

f (x) = 5

.

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Rewriting as y=mx+b

Rewrite the equation

3 x - 2 y = 6

in the form

y = m x + b

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Solving Function Systems

Solve the following system of functions:

f (x) = 3 x + 2

and

g (x) = 2 x - 1

.

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Find the Behavior (Leading Coefficient Test)

For the function

y = (x - 8) (x + 2)

, its

y

-intercept is its

x

-intercepts are

x =

Note: If there is more than one

x

-intercept write the

x

-values separated by commmas. When

x \to \infty, y \to

\infty

(Input + or - for the answer) When

x \to - \infty, y \to

\infty

(Input + or - for the answer)

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Determining Odd and Even Functions

Determine whether the function

f (x) = x^{3} + 2 x

is odd, even, or neither.

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Finding the Antiderivative

on

f (x) = \frac{x}{3} + 10

, find

f^{- 1} (x)

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Describing the Transformation

5. Suppose that the graph of the function

f (x) = 2 x^{2}

is reflected in the

x

-axis, translated 2 units to the left, and then translated 5 units upward. What could the equation of the quadratic function of the resultant graph be? A.

f (x) = - (x + 2)^{2} + 5

B.

f (x) = 2 (- x - 2)^{2} + 5

C.

f (x) = - 2 (x - 2)^{2} + 5

D.

f (x) = - 2 (x + 2)^{2} + 5

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Graphing

Given the piecewise function

f (x) = {\begin{cases} x & if & x < 2 \\ - x + 4 & if & x \geq 2 \end{cases}

Graph the function. Note: Be sure to include closed or open dots, but only at breaks in the graph. Arrows are assumed if no end symbols are shown.

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Finding the Symmetry

Determine whether the function f(x) = x^3 - 3x is odd, even, or neither.

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Arithmetic of Functions

Evaluate the function

h (x) = x^{4} - 4 x^{2} + 5

at the given values of the independent variable and simplify. a.

h (- 2)

b.

h (- 1)

c.

h (- x)

d.

h (3 a)

a.

h (- 2) = 5

(Simplify your answer.) b.

h (- 1) = ◻

(Simplify your answer.) c.

h (- x) = ◻

(Simplify your answer.) d.

h (3 a) = ◻

(Simplify your answer.

)

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Finding Roots Using the Factor Theorem

Find the roots of the function

f (x) = x^{3} - 9 x^{2} + 23 x - 15

using the factor theorem.

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Finding All Possible Roots/Zeros (RRT)

Find all possible roots/zeros of the function

f (x) = x^{3} - 4 x^{2} + x + 6

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Determine if Injective (One to One)

Determine whether the function is one-to-one. If it is, find a formula for its inverse.

f (x) = x^{3} - 1

Is the function one-to-one? Yes No Select the correct choice below and fill in any answer boxes within your choice. A. The inverse function is

f^{- 1} (x) =

B. There is no inverse function.

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Determine if Surjective (Onto)

Given the function

f : R \to R

defined as

f (x) = x^{2}

, determine if this function is surjective (onto).

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Finding the Vertex

Find the vertex of the function

f (x) = 2 x^{2} - 4 x + 1

.

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Finding the Sum

Hallar el

9 .^{\circ}

término de la sucesión geométrica cuya razón común es

\frac{1}{3}

y cuyo primer término es 2 .

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Finding the Difference

Let

f (x) = x^{2}

. How do the values of

f (2)

and

f (2) + 5

differ?

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Finding the Product

Find the product of the functions

f (x) = 3 x + 2

and

g (x) = 2 x - 5

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Finding the Quotient

Find the quotient of the functions

f (x) = 2 x^{2} + 3 x - 2

and

g (x) = x - 1

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Finding the Domain of the Difference of the Functions

Find the domain of the difference of the functions

f (x) = \sqrt{x}

and

g (x) = \frac{1}{x - 2}

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Finding the Domain of the Product of the Functions

Given the functions

f (x) = \sqrt{x}

and

g (x) = \frac{1}{x}

, find the domain of the product of the functions

h (x) = f (x) g (x)

.

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Finding the Domain of the Quotient of the Functions

Find the domain of the quotient of the functions

f (x) = x^{2} - 4

and

g (x) = x - 2

.

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Finding Roots (Zeros)

Find the roots of the function

f (x) = 2 x^{2} + 3 x - 2

.

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Identifying Zeros and Their Multiplicities

Find the zeros and their multiplicities for the function

f (x) = 2 x^{3} - 3 x^{2} - 11 x + 6

.

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Finding the Bounds of the Zeros

Find the bounds of the zeros of the function

f (x) = x^{3} - 7 x^{2} + 14 x - 8

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Proving a Root is on the Interval

Prove that the function

f (x) = x^{2} - 4 x + 4

has at least one root in the interval

[1, 2]

.

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Finding the Average Rate of Change

Aysha has a big backyard garden. When she measured the height of the tree, it was 14 feet tall. After one year, it was 16 feet tall. Assuming that the tree grows constantly at this rate. Determine the function that represents the height

(H)

of the tree each year. a.

H (y) = 15 + y

b.

H (y) = 14 + 2 y

c.

H (y) = 16 + y

d.

H (y) = 16 - 2 y

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Finding the Inverse

The following functions are inverses of each other.

f (x) = 5 x - 9

and

g (x) = \frac{x + 5}{9}

False

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Finding Maximum Number of Real Roots

What is the maximum number of real roots for the function

f (x) = x^{5} - 4 x^{3} + 2 x^{2} - 8

?

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Function Composition

Let

h (x) = 4 x + 1

. Find

(h \circ h) (x)

(h \circ h) (x) =

type your answer...

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Rewriting as a Function

Introduction to Functions: Vocabulary Given the function

L (S) = c

, which of the following statements are true? Check all that are correct.

L

is the name of the function,

c

is the independent variable and

S

is the dependent variable.

L

is the name of the function,

S

is the input variable, and

c

is the output variable.

L

is the name of the function,

S

is the independent variable and

c

is the dependent variable.

c

is the name of the function,

S

is the dependent variable and

L

is the independent variable

c

is the name of the function,

S

is the input variable, and

L

is the output variable.

C

is the name of the function,

L

is the dependent variable and

S

is the independent variable

L

is the name of the function,

c

is the input varisble, and

S

is the output variable.

c

is the name of the function,

c

is the dependent Variable, and

S

is the Independent Variable.

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Finding the Domain and Range

The graph below shows the relationship between minutes left and days of the month of your cellular phone plan. The relationship can be modeled by the equation

f (x) = - \frac{5}{2} x + 60

, where

y

is the number of minutes left and

x

is the day of the month. Which statement is true? There is no

x

-intercept or

y

-intercept. The domain is all real numbers. The range is all whole numbers greater than or equal to 0 and less than or equal to 60 The function has no maximum value.

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Determining if a Function is Rational

The function in the table is quadratic:

Unknown environment 'tabular'

True False

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Determining if a Function is Proper or Improper

Determine whether the following function is proper or improper:

f (x) = \frac{4 x^{2} + 5 x + 2}{2 x^{2} + 3 x + 1}

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Maximum/Minimum of Quadratic Functions

Find the maximum value of the quadratic function

f (x) = - 2 x^{2} + 4 x + 3

.

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Finding the Slope

What is the slope of the line represented by the function

f (x) = 7 x - 3

?

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Determining if Linear

Rewriting as an Equation

Rewriting as y=mx+b

Solving Function Systems

Find the Behavior (Leading Coefficient Test)

Determining Odd and Even Functions

Finding the Antiderivative

Describing the Transformation

Graphing

Finding the Symmetry

Arithmetic of Functions

Finding Roots Using the Factor Theorem

Finding All Possible Roots/Zeros (RRT)

Determine if Injective (One to One)

Determine if Surjective (Onto)

Finding the Vertex

Finding the Sum

Finding the Difference

Finding the Product

Finding the Quotient

Finding the Domain of the Difference of the Functions

Finding the Domain of the Product of the Functions

Finding the Domain of the Quotient of the Functions

Finding Roots (Zeros)

Identifying Zeros and Their Multiplicities

Finding the Bounds of the Zeros

Proving a Root is on the Interval

Finding the Average Rate of Change

Finding the Inverse

Finding Maximum Number of Real Roots

Function Composition

Rewriting as a Function

Finding the Domain and Range

Determining if a Function is Rational

Determining if a Function is Proper or Improper

Maximum/Minimum of Quadratic Functions

Finding the Slope

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