Algebra 1 Functions Unit Review

Functions Review

function (yes/no)
function notation
evaluating functions
function operations
domain and range

What is a function?

​Function vs. Relation

A function means that every x-value has EXACTLY one y-value.

​We are looking to see if the x values REPEAT!

Multiple Choice

Does this graph represent a function?

• Yes

• No

Multiple Choice

Does this mapping represent a function?

• Yes

• No

Multiple Choice

Do these ordered pairs represent a function?

• Yes

• No

Multiple Choice

Does this table represent a function?

• Yes

• No

Multiple Choice

Does this graph represent a function?

• Yes

• No

Multiple Choice

Does this mapping represent a function?

• Yes

• No

Multiple Choice

Does this table represent a function?

• Yes

• No

Multiple Choice

Does this graph represent a function?

• Yes

• No

Multiple Choice

Does this mapping represent a function?

• Yes

• No

Multiple Choice

Does this mapping represent a function?

• Yes

• No

Multiple Choice

Does this graph represent a function?

• Yes

• No

We replace the input or the output and solve for the missing piece.

f(4) this means that the x=4.
f(n)=4 this means that output is 4.

Evaluating

We give functions a name... f(x) means f of x.

The variable in the parentheses has to match the variable in the expression.

Naming Functions

Evaluating Functions

Math Response

Find f(4) .

f(x)=x² + 2

Type answer here

Correct Answer: 18

Deg^°

Rad

Math Response

Find f(-3).

f(x)=x²+2

Type answer here

Correct Answer: 11

Deg^°

Rad

Math Response

Find f(-8).

f(x)= x² - 3x

Type answer here

Correct Answer: 88

Deg^°

Rad

Math Response

Find the value of n if f(n)=40.

f(x)=5x+10

Type answer here

Correct Answer: 6

Deg^°

Rad

Math Response

Find the value of n if f(n)=-14.

f(x)= 2x+8

Type answer here

Correct Answer: -11

Deg^°

Rad

Multiple Choice

f(x)= 2x+5 and g(x)= 3x-9

What is f(x) + g(x)?

• 5x+5

• x+4

• 5x-4

• 2x+5

Multiple Choice

f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)

• 4x²+24
• 4x²+20x+24
• 4x²+12x+24
• 4x²+4x+24

Multiple Choice

f(x)=x²+1
g(x)=2x-5
Find f(x)-g(x)

• x²-2x+6
• -x²+2x+4
• -x²-2x-6
• x²-2x-4

Multiple Choice

f(n)= 2n + 1

g(n)= 3n

Find f(n) + g(n)

• 5n + 1

• -5n + 1

• -2n + 1

• -6n - 1

Multiple Choice

Given two functions:

$$g\left(x\right)\ =\ -x^2+4x$$  

$$h\left(x\right)=x+3$$  

Find $$g\left(x\right)-h\left(x\right)$$  

• $$x^2-3x+3$$  

• $$x^2+3x+3$$  

• $$x-2$$  

• $$-x^2+3x-3$$  

Multiple Choice

Add or Subtract to Simplify:
(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2 
• x + 2
• 2x² + x - 10 
• x - 10 

Multiple Choice

( 5x² + 8x + 7 ) - ( 2x² + 2x + 2 )

• 7x² + 10x + 8

• -3x² - 6x - 5

• 3x² + 6x + 5

Multiple Choice

Subtract: (2a² + 5a + 3) - (a² - 3a - 4)

• 3a² + 2a - 1
• a² + 8a + 7
• 3a² + 8a + 7
• a² + 2a - 1

Multiple Choice

(x-3)(x²+2x+7)

• x³-x²+x-21
• x³+5x+13x-21
• x³-3x²+7x-21
• x²+2x-3

Multiple Choice

What is the perimeter of the rectangle?

• $$25x^{2\ }-\ 20x$$  

• $$10x-4$$  

• $$20x\ -\ 8$$  

• 44

the set of y-values

how far down and up the graph goes

output

Range

The set of x-values

How far left and right the graph goes

input

Domain

Domain and Range

Multiple Choice

Find the DOMAIN

• {-5, -2, 1, 4}

• {1, -2, 4, -5}

• {-1, 0, 2, 3}

• {0, -1, 2, 3}

Multiple Choice

Find the RANGE

• {-5, -2, 1, 4}

• {1, -2, 4, -5}

• {-1, 0, 2, 3}

• {0, -1, 2, 3}

Multiple Choice

What is the domain of this graph?

• {-2 ≤ x ≤ 4}

• {-5 ≤ x ≤ 4}

• {-4, 0, -2}

• {-4 ≤ x ≤ 2}

Multiple Choice

What is the RANGE of this graph?

• -7 < x < 5

• -7 ≤ y < 5

• -3 < x < 1

• -3 ≤ y < 1

Multiple Choice

What is the DOMAIN of this graph? 
Remember DOMAIN is "x" values that go left to right. 

• -4 ≤ x ≤ 3
• -1 ≤ x ≤ 4
• 4 < x < 3
• -1 < x < 4

Multiple Choice

What is the range of the graph?

• y ≥ -6

• -7 ≤ y ≤ 3

• -8 ≤ y ≤ 4

• y ≤ -6

• All real numbers

Multiple Choice

What is the domain of the graph?

• x ≥ -6

• -7 ≤ x ≤ 3

• -8 ≤ x ≤ 4

• x ≤ -6

• All real numbers

Multiple Choice

What is the Range?

• y ≥ 6
• y ≤ 6
• -10 ≤ y ≤ 6
• -10 ≤ x ≤ 6

Multiple Choice

What is the range of the graph?
Remember: Range is y! 

• 1 ≤ x ≤ 5
• 1 < x < 5
• 1 ≤ y ≤ 5
• 1 < y < 5

Multiple Choice

What is the DOMAIN of this graph?

• -4 ≤ x ≤ 3

• -1 ≤ x ≤ 4

• 4 < x < 3

• -1 < x < 4

Multiple Choice

Before a bowler rolls her first ball, 10 pins are standing. The number of pins that will be left standing, y, is a function of the number of pins she knocks down. What is the range of the function?

• {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
• {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
• y ≤ 10
• 0 ≤ y ≤ 10

Multiple Choice

• (-∞, ∞)
• [-2, 2]
• (-2, 2)
• [-5, 5]

Multiple Choice

• [-3, 2)
• (-4, 2]
• (-5, 2]
• [-4, 2]

Multiple Choice

Each graph represents a relation. Determine the domain and range.

• Domain: [-7,5]

  Range: [-3,5]

• Domain: [-3,5]

  Range: [-7,5]

• Domain: (-3,5)

  Range: (-7,5)

• Domain: (-7,5)

  Range: (-3,5)

Multiple Choice

The height in inches of concrete being poured for a foundation can be found using the function y=15+2.5x, where x is the number of minutes. If the concrete is poured between 5 and 10 minutes, find the domain and range of this situation.

• Domain: $$5\le x\le10$$ Range: $$27.5\le y\le40$$

• Domain: $$27.5\le x\le40$$ Range: $$5\le y\le10$$

• Domain: {5, 6, 7, 8, 9, 10} Range: {28, 29, 30, ..., 40}

• Domain: {28, 29, 30, ..., 40} Range: {5, 6, 7, 8, 9, 10}

Multiple Choice

Mae worked at a summer camp where she earned $20 plus $7 an hour each week. The amount of money she earned each week, e, is a function of the number of hours she works, h. Mae could not work more than 20 hours each week.

What is the domain/range? Note: Mae can work part of an hour.

• Domain: {0, 1, 2, 3, ..., 20}

  Range: {20, 27, ..., 160}

• Domain: {20, 27, ..., 160}

  Range: {0, 1, 2, 3, ..., 20}

• Domain: $$0\le x\le20$$

  Range: $$20\le y\le160$$

• Domain: $$20\le x\le160$$ Range: $$0\le y\le20$$

Multiple Choice

Lucy's dog gave birth to a litter of 7 puppies. She plans to sell each puppy for $350. The function f(x)=350x can be used to represent this situation. What is the domain/ range of this function?

• Domain: {0, 1, 2, 3, 4, 5, 6, 7}

  Range: {0, 350, 700, 1050, 1400, 1750, 2100, 2400}

• Domain: {0, 350, 700, 1050, 1400, 1750, 2100, 2400}

  Range: {0, 1, 2, 3, 4, 5, 6, 7}

• Domain: $$0\le x\le2400$$ Range: $$0\le y\le7$$

• Domain: $$0\le x\le7$$ Range: $$0\le y\le2400$$

Multiple Choice

Leslie's car travels about 25 miles per gallon of gas.

This situation can be represented by the function f(x) = 25x

Her car needs 14 gallons of gas to be full. What is a reasonable DOMAIN?

• $$x\ge25$$

• $$0\le y\le14$$

• $$x\le14$$

• $$0\le x\le14$$

Multiple Choice

The booster club is selling school t-shirts for $10 each. Their initial cost to buy 30 t-shirts was $150. The profit, p, on the 30 shirts is a function of the number of t-shirts sold, t, can be found using the function p=10t-150.

Identify whether this is continuous or discrete and the domain/range.

• Continuous
  Domain: $$0\le x\le30$$

  Range: $$-150\le y\le150$$

• Continuous

  Domain: $$-150<-x\le150$$
  Range: $$0\le y\le30$$

• Discrete

  Domain: {0, 1, 2, 3, 4, 5, ..., 30}
  Range: {-150, -149, -148, ..., 150}

• Discrete

  Domain: {-150, -149, -148, ..., 150}
  Range: {0, 1, 2, 3, ..., 30}