Unit 4 Summative Recovery

Category: Graphs

What is the value of f(4)?

Mathematical Equivalence

ON

Answer explanation

Graph points are (x, y) pairs

Notation f(4) is when x = 4

----- ----- ----- -----

Find pair (4, 40)

Here, x = 4 and y = 40

----- ----- ----- -----

Answer is 40

Category: Graphs

The graphic represents early infection rates of coronavirus in March 2020. Initial infections at the start were 16. What is the context of the range?

• Infections days after March 1st, 2020

• x > 0

• (0, ꝏ)

• Daily new confirmed covid-19 cases

• (16, ꝏ)

Answer explanation

Domain= (lowest x, highest x)

Range= (lowest y, highest y)

----- ----- ----- -----

The context for domain and range is found by reading the axis labels on the graphic

----- ----- ----- -----

Domain context = infections days after March 1st, 2020

Domain = x > 0

Domain = (0, ꝏ)

----- ----- ----- -----

Range context = daily new confirmed covid-19 cases

Range = (16, ꝏ)

Category: Graphs

Which of the following is true about the graph?

(select all that apply)

• Growth

• Decay

• y = 2(b)^x + 0

• Decreasing

• y = a(2)^x + 0

Answer explanation

y = a(b)^x + k

----- ----- ----- -----

a = 2 (y-intercept on graph)

k = 0 (flat portion on graph)

----- ----- ----- -----

y = 2(b)^x + 0

----- ----- ----- -----

Domain is (-ꝏ, ꝏ)

Range is (0, ꝏ)

Category: Graphs

As x → -ꝏ, f(x) → ?

• -4

• -ꝏ

• ꝏ

Answer explanation

Notation "x → -ꝏ" asks you to look at left portion of graph

----- ----- ----- -----

On the left, the graph is flat

----- ----- ----- -----

The question is really just asking the asymptote value

----- ----- ----- -----

f(x) will approach -4

Category: Graphs

A person begins a leg workout with 100% of their energy. After each squat set their energy falls by a certain percentage. Select the range.

(click graph to enlarge)

• (-ꝏ, ꝏ)

• (-ꝏ, 100)

• (0, 7.7)

• (0, 100)

Answer explanation

Graph range= (-ꝏ, 100)

But this is not the answer!

----- ----- ----- -----

Remember that word problems can change range and domain values

----- ----- ----- -----

Range context= y-axis label of "energy left"

----- ----- ----- -----

Range= (0, 100)

The person starts with 100% of their energy and exercises until they have 0% left

Category: Equation

f(x) = a(b)^x

What is the value for a from the table?

Mathematical Equivalence

ON

Answer explanation

y = a(b)^x

----- ----- ----- -----

Recall the "FIRE" acronym

F → y = final value

I → a = initial value

R → b = rate

E → x = time

----- ----- ----- -----

"a" is the value next to where x = 0 on the table

----- ----- ----- -----

a = 0.25

----- ----- ----- -----

y = 0.25(b)^x

Category: Equation

f(x) = a(b)^x

What is the value for b from the table?

Mathematical Equivalence

ON

Answer explanation

y = a(b)^x

----- ----- ----- -----

Recall the "FIRE" acronym

F → y = final value

I → a = initial value

R → b = rate

E → x = time

----- ----- ----- -----

"b" is the number you multiply for the next y-value

----- ----- ----- -----

a = 0.25

b = 4

----- ----- ----- -----

y = 0.25(4)^x

Category: Equation

A Petri dish currently has 100 bacteria. Each hour, the total number doubles. Write an equation that models this situation.

• y= 100 + 2x

• y= 100(2)^x

• y= 2 + 100x

• y= 2(100)^x

Answer explanation

a = 100

b = double = 2

----- ----- ----- -----

y = 100(2)^x

Find the average rate of change from the interval (0, 2)

(click on graph to enlarge)

Mathematical Equivalence

ON

Answer explanation

Find the average rate of change from the interval (1, 2)

(click on graph to enlarge)

Mathematical Equivalence

ON

Answer explanation