Functions and Relations

Graphs

100

Using your calculator determine the minimum of f(x) = x^2

minimum is 0

200

Determine the minimum value of f(x) = x^2 - 4

minimum is -4

300

Is x^3 - 5 a function?

Graph it in Desmos to find out.

Yes

400

If a graph went from an x-value of -4 and went to an x-value of 10, what would the domain be in interval notation?

{-4<x<10}

500

If a graph went from a y-value of 3 to a y-value of 17, what would the range be in interval notation?

{3<y<17}

???Mystery???

100

Evaluate f(5) for the function below f(x) = 3x - 2

f(5) = 13

200

Evaluate f(x) = x^2 - 3x + 6, when x = -3

f(-3) = 24

300

If f(x)= x^2 - 3x + 5, find the value of f(3)

f(3) = 5

400

If f(x)=4x-5

What is the domain value when the range value is 3?

2

500

If f(x)=3x+2

Find f(7)

f(7)=23

Is It a Function?

100

The name of the test used to determine whether a graph is a function or not is called the ____________ _______ test.

What is the vertical line?

200

A function is a special type of relation where every _____________ value has exactly one ________________ value. Fill in the blank

input output

300

Determine if the following relation is a function. Show your work using a table to list the order pairs. {(9, 0), (3, 0), (2, 2), (-3, -4)} Explain your reasoning

Yes, the x-values do not repeat.

400

Removing which ordered would make this relation a function {(-9,2), (4,5), (3,5), (7, 2), (-9,5)} 1) (4,5) 2) (7, 2) 3) (3,5) 4) (-9,2) Explain

(-9,2) because the the input -9 will no longer have two outputs

500

Does this relation represent a function?

(3,2) (4,8) (5,7) (3,4)

NO!

Relations/Domain and Range

100

The domain of the relation {(1,0), (-2, 3), (3, 4)} would be:

What is {1, -2, 3}?

200

Write the range of this relation: {(8,7), (-6, 3), (2, 0)}

What is {7, 3, 0}?

300

What is the range of function f(x) = 2x - 8 when x = 2, 6, and 10?

Range= {-4, 4, 16}

400

Create a mapping chart for the ordered pairs {(0, 4), (-7, 5), (8, 3), (-7, 2)} Then, determine the domain and range of this relation.

Domain- {-7,0,8} Range- {2,3,4,5}

500

The function h(t) = −16t^2 + 144 represents the height, h(t), in feet, of an object from the ground at t seconds after it is dropped. A realistic domain for this function is... 1 −3 ≤ t ≤ 3 2 0 ≤ t ≤ 3 3 0 ≤ h(t) ≤ 144 4 all real numbers

Choice 2

Vocabulary

100

The name of the horizontal axis is called ______________.

What is the x-axis?

200

Another name for the coordinates (0,0) would be the _______________.

What is the origin?

300

A set of ordered pairs is called a _______________.

What is a relation?

400

What is the name of a function that has at least two rules?

Piecewise functions

500

List 2 different names for a function x-values List 2 different names for a functions y-values

x-values inputs domain y-values: outputs range