Characteristics of Functions

Characteristics of

Functions

• F(x)=

• y=

• X-intercept: zero

• Y-intercept: initial value

Key words:

• Represents

• Models

• Supports

• Transform

Linear Functions

​Slope, m

Multiple Choice

The graph of a linear function is shown on the coordinate plane. Which function best represents the relationship shown in the graph?

• $$y=2x-4$$

• $$y=2x+2$$

• $$y=\frac{1}{2}x-4$$

• $$y=\frac{1}{2}x+2$$

Multiple Choice

The graph of a linear function is shown on the grid. Which statement is best supported by the graph of the function?

• The slope of the graph is $$\frac{1}{2}$$ .

• The x-intercept of the graph is 6.

• The zero of the function is $$\frac{1}{2}$$

• The y-intercept of the graph is 6.

Multiple Choice

A line is graphed on a coordinate grid. Which statements best describe the line?

• Equation x=6

  Slope: 0

• Equation y=6

  Slope: undefined

• Equation y=6

  Slope: 0

• Equation x=6

  Slope: undefined

Drag and Drop

The tables of ordered pairs represent some points on the graphs of two lines. Which system of equations is represented by the two lines?

Line 1: ​

Placeholder

Line 2: ​

Placeholder

​

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y=5x-7

4x+y=12

y=7x-9

4x-y=4

Multiple Choice

The table represents some points on the graph of a linear function. Which function represents this relationship?

• $$y=-\frac{4}{7}x+\frac{23}{7}$$

• $$y=-\frac{4}{7}x+\frac{31}{7}$$

• $$y=\frac{19}{7}x+\frac{8}{7}$$

• $$y=\frac{19}{7}x+\frac{46}{7}$$

Multiple Choice

The function f(x) = x was transformed to form g(x) = f(x) - 23. Which statement is true about the graphs of f and g ?

• The graphs of f and g are not parallel, and the graph of f is translated 23 units up to create the graph of g.

• The graphs of f and g are not parallel, and the graph of f is translated 23 units down to create the graph of g.

• The graphs of f and g are parallel, and the graph of f is translated 23 units up to create the graph of g.

• The graphs of f and g are parallel, and the graph of f is translated 23 units down to create the graph of g.

• F(x)=

• y=

• X-intercept: zero

• Y-intercept: initial value

Key Terms:

• Axis of Symmetry, x=

• Vertex (x,y)

• Minimum (y-value)

• Maximum (y-value)

• Represents

• Models

• Supports

• Transform

Quadratic Functions

Hotspot

A graph of a quadratic function is shown. What are the x-intercepts of the function? Select TWO correct answers.

Multiple Choice

Quadratic function f has a vertex (4,15) and passes through the point (1,20). Which equation represents f ?

• $$f\left(x\right)=-\frac{5}{9}\left(x-4\right)^2+15$$

• $$f\left(x\right)=\frac{5}{9}\left(x-4\right)^2+15$$

• $$f\left(x\right)=-\frac{35}{9}\left(x-4\right)^2-15$$

• $$f\left(x\right)=\frac{35}{9}\left(x-4\right)^2-15$$

Drag and Drop

Which statement is best supported by the graph?​

Placeholder

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The equation of the axis of symmetry is x=-3

The minimum value of the function is 9.

The vertex of the graph is (9,-3).

The function has a zero at 6

​​Plus and Minus Symbol

Multiple Choice

Which statement about $$f\left(x\right)=12x^2-36x+27$$ is true?

• The zeros are $$\pm\frac{2}{3}$$ because f(x)=3(2x-3)(2x+3).

• The zeros are $$\pm\frac{2}{3}$$ because f(x)=3(2x-3)(2x+3).

• The only zero is $$\frac{2}{3}$$ because $$f\left(x\right)=3\left(2x-3\right)^2$$

• The only zero is $$\frac{3}{2}$$ because $$f\left(x\right)=3\left(2x-3\right)^2$$

Dropdown

The function $$f\left(x\right)=x^2$$ was transformed to create the function $$g\left(x\right)=f\left(x-2\right)+5$$ . Complete the sentence about the transformation.



The graph of f is translated 2 units ​

Select answer

and 5 units ​

Select answer

to create the graph of function g.

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​

​Exponential Functions

• F(x)=

• y=

• X-intercept: zero

• Y-intercept: initial value

• Asymptote, y=

• Represents

• Models

• Supports

• Transform

Exponential Functions

Key Terms:

Graphing

Which graph represents $$f\left(x\right)=3\left(\frac{2}{3}\right)^x$$ ?

Multiple Choice

Which statement about the graph of the function $$f\left(x\right)=35\left(1.4\right)^x$$ is true?

• The y-intercept of the function is (0,35).

• The x-intercept of the function is (1.4,0).

• The graph of hte function is decreasing for all values of x.

• The asymptote of the function is y=0.4.

Multiple Choice

New houses are being built in a neighborhood. The table shows the exponential change in the number of houses over the last 6 years. Which exponential function best models the data?

• $$f\left(x\right)=1.4\left(18.9\right)^x$$

• $$f\left(x\right)=27\left(1.3\right)^x$$

• $$f\left(x\right)=18.9\left(1.4\right)^x$$

• $$f\left(x\right)=1.3\left(27\right)^x$$

Match

A company started with 40 employees. The number of employees at the shipping company increases at a rate of 7.5% each year. Match the numbers with their significance in the growth equation $$y=a\left(1+\frac{r}{100}\right)^x$$ .

• Y- Intercept, a

• Growth/Decay

• % increase or decrease

• Number of Years

• Number of Employees

40

+

.075

x

f(x)

• 40

• +

• .075

• x

• f(x)