Characteristics of Linear Functions

Linear Functions Characteristics Review

​Let's Look at an Example....

​You can use your notes and understanding of linear characteristics to find information about a certain linear function. Watch the video on the next slide to see this in action!

Multiple Choice

Which graph is linear?

• Graph A

• Graph B

• Graph C

• Graph D

Multiple Choice

Write the equation of the line.

• y = -1/3x - 2

• y = 1/3x - 2

• y = 3x - 2

• y = -3x - 2

Multiple Choice

Consider the equation: y=-x+4 Identify the slope and y-intercept.

• m=4, b=-x

• m=-x, b=4

• m=1, b=4

• m=-1, b=4

Discrete or Continuous Problems

Discrete or Continuous?

Discrete graphs have breaks in the domain. You have to pick up your pencil to draw. (Dots) In context these are items you can count (no in-between values)

​

Continuous graphs have not breaks in the domain. You can draw it without picking up your pencil. In context these are measurable values

Multiple Choice

Is this discrete or continuous?

• discrete

• continuous

Multiple Choice

Graph of the growth of a plant for the next 30 days. 

• Discrete

• Continuous

Multiple Choice

Discrete or continuous data?

• Discrete

• Continuous

Multiple Choice

The number of orange Skittles in a bag. 

• Discrete

• Continuous

Domain & Range Problems

Discrete Function

The points are separated.

List the x-values

List the y-values

Multiple Choice

Find the RANGE

• {-5, -2, 1, 4}

• {1, -2, 4, -5}

• {-1, 0, 2, 3}

• {0, -1, 2, 3}

Multiple Choice

Find the DOMAIN

• {-5, -2, 1, 4}

• {1, -2, 4, -5}

• {-1, 0, 2, 3}

• {0, -1, 2, 3}

This is a continuous function.

Use inequalities to list domain and range.

Interval Notation

• use a bracket [ ] for values that are defined (closed point)

• use parenthesis ( ) for values that are not defined (open point or arrow)

• List from smallest to largest, so for domain: left to right and for range: bottom to top

Inequality Notation

• For values that are defined

• For values that are not defined

• ​Use x for domain values, y for range values

Multiple Choice

What is the domain of the graph?

• -7 ≤ x < 5

• -3 ≤ x < 1

• -3 ≤ y < 1

• -7 ≤ y < 5

Multiple Choice

A student rode a bike from school to a recreation center. The graph shows the student’s distance in miles from the recreation center after riding the bike for x miles. What is the range of the situation?

• All real numbers greater than or equal to 0 and less than or equal to 28

• All real numbers greater than or equal to 0 and less than or equal to 9

• All real numbers less than 28

• All real numbers less than 9

Multiple Choice

Identify the Domain of the graph depicted.

• 0 ≤ x ≤ 180

• 0 ≤ y ≤ 180

• 0 ≤ x ≤ 1500

• 0 ≤ y ≤ 1500

Multiple Select

What is the domain & range for this graph?

[check all that apply]

• Domain: [0, 5]

• Domain: [1, 4]

• Range: [3, 15]

• Range: [0, 15]

Rate of Change (Slope) Problems

Multiple Choice

The line pictured has a(n) ______ slope.

• Undefined

• Zero

• Positive

• Negative

Slope on a Graph

Multiple Choice

Find the slope

• -2/3

• 3/2

• -3/2

• 2/3

Multiple Choice

What is the cost of one snack?

Find the ROC.

• m=$0.20 per snack

• m=$1.00 per snack

• m=$0.80 per snack

• m=$0.40 per snack

Slope from a Table

Multiple Choice

Find the slope.

• -2

• 2

• ¹/₂

• -¹/₂

Slope from Two Ordered Pairs

Multiple Choice

What is the slope of the line that passes through (-4, 0) and (-6,2)?

• ^-2/10

• -1

• -5

• 5

Slope/Rate of Change in Word Problems

• ​Look for "rate" keywords, what # is changing?

  ​

• Marci travels 65 miles per hour

• Daniel earns $14 per hour

• Sheila bakes 3 cookies per person

• Ground beef costs $4.50 for every pound

• ______per______ indicates a rate of change

• Could also be "each hat costs $14" or "car rental is $50 a day", etc.

Multiple Choice

The equation represents the amount of money in an account after x weeks. Interpret the slope.

$$y=25x+210$$  

• The amount of money increases by $25 each week.

• The amount of money increases by $1 every 25 weeks.

• The amount of money increases by $210 every 25 weeks.

Multiple Choice

Which of the following are ways to find the rate of change?

• change in y over change in x

• rise over run

• difference in y coordinates divided by the difference in x coordinates

• all of the above

X & Y Intercepts

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 y-intercept shown on the graph?

• (0, -2)

• (3, 0)

• (0, 3)

• None of these.

Multiple Choice

What is the x-intercept shown on the graph?

• (2, 0)

• (-2, 0)

• (0, 3)

• (3, 0)

Multiple Choice

What is the y-intercept?

• 12

• -3

• 8

• 0

Multiple Choice

What is the x-intercept?

• 12

• -3

• 8

• 0

Interpreting Intercepts

• The x-intercept means: they can buy 10 slices of pizza, but no donuts

• The y-intercept means: they can buy 20 donuts, but no pizza

Multiple Choice

Interpret the x-intercept

• (12, 0)

  After 12 haircuts, Adrienne will make a profit of $0

• (0, –200)

  Before any haircuts are given, Adrienne's starting profit is –$200

Multiple Choice

Dorothy loves to make cakes.  The following table shows how the number of eggs that she has left changes as she makes cakes. What is the meaning of the y-intercept?

• She uses 5 eggs for every 2 cakes.

• She started with 47 eggs.

• She uses 47 eggs for every 0 cakes.

• She started with 5 eggs.

Interval of Increase/Decrease & End Behavior

Increasing, Decreasing or Constant

Linear functions are either always increasing, always decreasing, or constant.

​

Multiple Choice

In this graph INCREASING, DECREASING or CONSTANT?

• Increasing

• Decreasing

• Constant

Multiple Choice

Which statement is true about this graph?

• This function is always constant

• This function is always increasing

• This function is never increasing

• This function is both increasing and decreasing

Multiple Choice

When is the function decreasing?

Use the x-values

• (30, 55)

• (40, 60)

• (15, 40)

• (60, -40)

Multiple Choice

What is the decreasing interval on the function shown?

• $$\left(-\infty,\ -3\right)$$

• $$\left(-\infty,\ -4\right)$$

• $$\left(-4,\ \infty\right)$$

• $$\left(-3,\ \infty\right)$$

Multiple Choice

Which one means left

• x →-∞

• x →∞

Multiple Choice

$$Which\ of\ the\ following\ indicates\ that\ as\ x\ moves\ left\ you\ moves\ up?$$  

• $$As\ f\left(x\right)\longrightarrow\infty,\ f\left(x\right)\longrightarrow\infty$$  

• $$As\ x\ \longrightarrow-\infty,\ f\left(x\right)\longrightarrow-\infty$$  

• $$As\ x\longrightarrow-\infty,\ f\left(x\right)\longrightarrow\infty$$  

Multiple Choice

Which one means the function goes down on the left

• x →-∞, y→∞

• x →-∞, y→-∞

​THE END

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