Comparing Functions Review

Comparing Functions Review

Unit 7: Mr. Schulz's Algebra 1B

Piecewise-Defined Functions

• A function where segments of the domain are defined by different functions

• Remember our friend Miriam at the Vet's office? There were different rules for feeding different size dogs.

• The same goes for different pricing structures (the mixed nuts problem)

Multiple Choice

What is g(7) if:

• -17

• -13

• 13

• 17

Multiple Choice

Find f(0)

• -3

• 18

• 4

• 0

Comparing Functions

• Two major components to functions: Rate of Change (slope) and Starting value (y-intercept)

• At the starting value (x = 0), one function may be higher, lower, or the same as another.

• What matters is how the functions (output) act at all other x-values (inputs)

Comparing Functions Example

• Suppose you are traveling to St. Louis from St. Anne by car (250 mi)

• There are different places where the Speed Limit changes from 55 mph to 70 mph

• If we are comparing TIME (t) to DISTANCE TO ST. LOUIS (d), we can create a function using the two extremes in speed

• The two drives can be compared using t as an input and d as the output.

• Faster drive: d = 250 - 70t

• Slower drive: d = 250 - 55t

Multiple Choice

Dave owns a lawn business. He charges $10 per hour and a $25 dollar disposal fee. What is the correct equation Dave would use to find out how much to charge his customers?

• y = 25x + 10

• x = 25y + 10

• y = 10x +25

• x = 10y + 25

Multiple Choice

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Which service is cheaper for 8 movies in one month?

• Beth's service ($38 vs. $40) is cheaper

• Nate’s service ($42 vs. $44) is cheaper

• Nate’s service ($38 vs. $40) is cheaper

• Beth's service ($42 vs. $44) is cheaper

Multiple Choice

Which company shows a greater rate of change?

• Water's Edge Rafts

• Ryan's Rafts

Multiple Choice

Which company should you use if you rent the raft for 9 hours?

• Water's Edge Rafts

• Ryan's Rafts

Multiple Choice

The graph shows the race between the tortoise and the hare. How much of a head start did the hare give the tortoise?

• 2 minutes

• 4 minutes

• 7 minutes

• 10 minutes

Linear Inequalities

• Shading a region of the x-y coordinate plane (half-plane) rather than a segment of a number line

• Start by rewriting the inequality in slope-intercept form (y = mx + b) (essentially solve for y)

• Where you shade and which line is the border all depends on the type of inequality sign

•  $\ge\ and\ \le$  mean a SOLID boundary line,  $<\ and\ >$  mean a DASHED boundary line

•  $<\ and\ \le$  mean shade the region BELOW the y-intercept,  $>\ and\ \ge$  mean shade the region ABOVE the y-intercept

• 
  

Multiple Choice

Select the graph for y ≥ -3.

• A

• B

• C

• D

Multiple Choice

How would you graph the following linear inequality?

y ≥ 4

• Dashed line, shade above

• Dashed line, shade below

• Solid line, shade above

• Solid line, shade below

Multiple Choice

Which of the following equations match the given graph?

• y ≥ (2/5)x + 1
• y ≥ (-2/5)x + 1
• y ≤  (2/5)x + 1
• y ≥ (-2/5)x - 1

Multiple Choice

Consider the function y < 2x+3. Which is true?

• The line would be solid with shading above.

• The line would be dashed with shading above.

• The line would be solid with shading below.

• The line would be dashed with shading below.