Unit 2 Review: Linear Functions

Unit 2 Review: Linear Functions

Match

Match the Graph with its slope.

Negative

Positive

Zero

Undefined

• Negative

• Positive

• Zero

• Undefined

Multiple Choice

Slope is know as

rise/______

• run

• fall

• none

• rise

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

• 3

• $$\frac{1}{3}$$

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$2\ \frac{1}{2}$$

• 2

Multiple Choice

In the equation y=mx+b, what does the m represent?

• slope
• y-intercept
• linear
• point-slope

Multiple Choice

What does 'b" represent in y=mx+b

• y-intercept
• macaroni
• nothing
• slope

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2
• 3
• 5
• Cannot be Determined 

Multiple Choice

What is the y-intercept of the line with the equation
$$y\ =\ -2x\ +\ 4$$  

• $$-2$$  

• $$2$$  

• $$4$$  

• $$-4$$  

Multiple Choice

Write a linear equation in slope intercept form of a line with a slope of 12 and y intercept of 10

• y=12x-10

• y=10x+12

• y=12x+10

• x=10x-12

Multiple Choice

Graph the line with the equation
$$y\ =\ -\frac{2}{3}x\ +\ 4$$  

Multiple Choice

Write the equation of the graph in slope-intercept form

• $$y=-2x-4$$

• $$y=2x\ -\ 4$$

• $$y=\frac{1}{2}x-4$$

• $$y=-\frac{1}{2}x-4$$

Multiple Choice

Write a equation:  A plumber charges $50 for a house call plus $12 per hour for labor.

• y = 50 x + 12
• y =12 x + 50
• y = 62 x
• x = 50 + 12y

X-intercepts are special!

They can also be called ZEROS

However, y-intercepts do not have any other names.

Finding x-intercepts

• Graph- Look to see were the graph crosses the x-axis

• Table- Find a value where y=0 (opposite)

• Equation- Use DESMOS! Then look at the graph

Finding y-intercepts

• Graph- Look to see were the graph crosses the y-axis

• Table- Find a value where x=0 (opposite)

• Equation- Use DESMOS! Then look at the graph

Multiple Choice

What is the x-intercept? (type table in DESMOS and look at graph)

• 12

• -3

• 8

• 0

Multiple Choice

What is the y-intercept?

• (0,7)

• (0, 0)

• (0,1)

• (0, 2)

Multiple Choice

Give the x-intercept

3x + 8y = 24

• (8, 0)

• (0, 8)

• (3, 0)

• (0, 3)

Multiple Choice

What is the y-intercept in the equation x + 2y = 4

• (0, 0)

• (0, 2)

• (4, 0)

• (2, 0)

• Move lines up/down on graph.

• Changes the y intercept (positive shifts up; negative shifts down).

• Called a Vertical Shift.

Translations - Vertical

• Flips the graph over the y-axis.

​

• Negative slope.​

• Forms an X.

Reflections

Multiple Choice

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

• Translation left 2 units
• Translation right 2 units
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Multiple Choice

How did the equation shift from the parent function?

y = f(x) + c

• Shifted up "c" units

• Shifted down "c" units

• Stretches vertically

• Shifted right "c" units

Multiple Choice

What is the linear parent function?

• y = x

• y = mx + b

• Ax + By = C

• $$y-y_1\ =\ m\left(x\ -\ x_1\right)$$

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = f(x) + 3. Describe the transformation.

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g shifted down 3 units

• Graph g shifted down 4 units

• Graph g shifted up 4 units

• Graph g reflected

Multiple Choice

Which represents the parent function shifted down two units?

• f(x) = -2x

• f(x) = x - 2

• f(x) = x + 2

• f(x) = 2x

Multiple Choice

How did the equation shift from the parent function? y=(x)+7

• Up 7
• Down 7
• Less steep
• Steeper

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

What are the two ways to transform a linear function?

• Changing the values of m and b

• Changing the sign of b

• Changing the values of x and y

• Changing the sign of x or y

Multiple Choice

How did the equation shift from the parent function y = x to y = x + 2?

• translated up 2

• translated down 2

• steeper

• translated right 2

Multiple Choice

In order to determine if the linear function has shifted up or down (translated,) we look at the _____ in the equation or on the graph.

• x-intercept

• y-intercept

• slope

• negative slope

Multiple Choice

In order to determine if the linear function has reflected (flipped), we look to see if the equation or graph has a ______.

• x-intercept

• y-intercept

• slope

• negative slope

Multiple Choice

The function f(x) = x

has been transformed to

g(x) = x - 5.

Which of the following describes the change?

• vertical shift up 5 units

• vertical shift down 5 units

• horizontal shift right 5 units

• horizontal shift left 5 units

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g shifted down 3 units

• Graph g shifted down 4 units

• Graph g shifted up 4 units

• Graph g reflected

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• Graph g is less steep.

• Graph g shifted down 1 unit

• Graph g is steeper.

• Graph g shifted up 2 units

Multiple Select

Select all the equations that are steeper than the parent function y = x.

• y = 3x + 5

• y = -x - 2

• y = 2x

• y = -1/2x

Multiple Select

Select all the equations that are less steep than then parent function y = x.

• y = 3x + 5

• y = 1/3x - 2

• y = 2x

• y = -1/2x

Definition

A RELATION is a set of ordered pairs (like the x-and y-coordinates are in a "relationship". In addition, all of the x-coordinates are called the DOMAIN and all of the y-coordinates are called the RANGE.

Example: Name the domain and range for this relation below

(-5, -3), (-2,0), (1,3), (4,6), (7,9)

Domain (all the x-values): {-5, -2, 1, 4, 7}

Range (all the y-values): {-3, 0, 3, 6, 9}

Multiple Choice

Which numbers make up the domain of this relation below:

(7, 5), (-3, 2), (1,- 1), (4, -6), (-2, 4)

• {1, 2, 3, 4, 5}

• { -3, 1, 7}

• {-3, -2, 1, 4, 7}

• {-6, -1, 2, 4, 7}

Functions

A relation can be any kind of relationship between sets of numbers, FUNCTIONs are a special kind of relationship where EVERY INPUT MUST HAVE EXACTLY ONE OUTPUT.

In other words, the x-value cannot repeat

Multiple Choice

Does the relation below a function:

{(–7, 4), (–8, 3), (–7, 7), (–20, 8), (5, 9), (3, 1), (2, 6)}

• Yes

• No

Multiple Choice

Does the relation below represent a function:

{(10, 9), (–2, –16), (–6, 7), (5, 8), (8, –16), (–11, 9)}

• Yes

• No

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Is the relation shown in the table a function?

• Yes

• No

Multiple Choice

What is range of the table?

• 0, 2, 10, 12

• -12, 13, 16

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D