Spartan Functions

General

100

This is the collection of all input values for a relation or function.

What is the Domain?

200

This represents the y-values or outputs of a relation or function.

What is the range?

300

This is used to determine if a graph is a function.

What is the vertical line test?

400

This is a relationship between two variables in which the input goes to exactly one output.

What is a function?

500

Evaluate  f(x) = x² + 3   for:

 f(x - 1)

What is f(x - 1) = x² -2x + 4

Key Features

100

Maximum and Minimum of the following Graph: https://images.flatworldknowledge.com/reddenint/reddenint-fig02_467.png

Max: Infinity Min: (2, -6)

200

Find the x and y intercepts and represent them as points: https://images.flatworldknowledge.com/reddenint/reddenint-fig02_467.png

x - intercepts: (-7, 0) and (4, 0) y - intercepts: (0, -4)

300

Find the domain and range of the following graph: https://images.flatworldknowledge.com/reddenint/reddenint-fig02_467.png

D: All Real Numbers or (-infinity, infinity) R: [-6, infinity)

400

Find the intervals of the graph where the function is increasing. Must name all the increasing intervals. https://images.flatworldknowledge.com/reddenint/reddenint-fig02_467.png

Increasing: [-5, -2[, (2, infinity)

500

Name the Domain and Range for the following Function: https://mathbitsnotebook.com/Algebra2/FunctionGraphs/PW3.gif

D: [-5, 1]U(2, 5] R: [-2, 4]

Interpreting Functions

100

This is what x represents in f(x).

What is the input?

200

This is what f(x) represents for a function.

What is the output?

300

This is the value of the output for f(2) on the following graph: https://mathbitsnotebook.com/Algebra1/FunctionGraphs/PW1.gif

What is f(2) = 4?

400

This is the input when f(x) = -2 on the following graph: https://mathbitsnotebook.com/Algebra1/FunctionGraphs/PW1.gif

What is x = -4?

500

The amount of money in Nicole's savings account can be modeled by a function. M(x) models the amount of money in the account when making x deposits. This is what the statement M(5) = 200 means.

What is Nicole has $200 after her 5th deposit?

Transformations

100

This value in the function below shifts the function left or right.

f(x) = a(bx - c)² + d

What is the value of "c"

200

The equation(in function form) representing the transformation of a linear parent function shifted 3 units up.

What is f(x) = x + 3

300

Function g(x) below shows these transformations compared to the absolute value parent function

g(x) = 2 | x - 3 |

What is vertical stretch by a factor of 2 and a horizontal shift of 3 to the right.

400

This function, g , represents a horizontal shift of right 2 units, a reflection over the x - axis, and a vertical shift down 4 for the given function below.

f(x) = | x - 1 | + 2

What is g(x) = - | x - 3 | - 2

500

This is the ordered pair,  given that (3,1) is a point on f(x) and :

y = 2f(x - 2)

What is (1, 2)

Notes

(x, y) = (x - 2, 2y) = (3-2, 2(1)) = (1, 2)

Random

100

This is the parent function for:

f(x) = -3x

What is f(x) = x

200

Daily Double!!!!

This would be the winner of a 2025 State Final Championship Soccer Game with the following match- up.       SLU vs. De Smet

Who is De Smet of course!

300

This is the function family of the following function.

f(x) = 2^x + 3

What is a Exponential?

400

This is the equation of a function that is described by the given characteristics:

f(x) = x² , moved 4 units to the left and 5 units down

What is f(x) = (x + 4)² - 5

500

If (-3,1) is a point of the graph y = f(x), what must be a point on the graph y = f(x + 2)?

What is the point (-1, 1)