Functions SBAC Practice

Kiki starts her run at 5:00 p.m.  Let f(t) represent Kiki’s speed, in miles per hour, t hours after she starts running for 0 ≤ t ≤ 4.  The following information holds for the function f:

f(1) = 5

f(4) = 2

f(2) = 8

f(1) < f(3)

Kiki’s fastest speed occurs at 7:00 p.m.  Given this information, which of the following must be true?  Select all that apply.

• At 8:00 p.m., Kiki’s speed was at least 5 miles per hour.

• At 6:30 p.m., Kiki’s speed was at most 8 miles per hour

• Kiki ran at most 32 miles.

Tags

CCSS.HSF.IF.B.4

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Billy buys light bulbs in packs of 8 for $20. The shipping cost is $10 regardless of the number of packs bought.  Billy has only $120 to spend.

If n is the number of packs of lightbulbs bought, then the cost per lightbulb, C, can be modeled as a function of n.  Select the statement that correctly descriptives the domain of the function.

• The domain is the set of all real numbers 1 ≤ n ≤ 6.

• The domain is the set of all real numbers 1 ≤ n ≤ 5.

• The domain is the set of all integers  1 ≤ n ≤ 6.

• The domain is the set of all integers 1 ≤ n ≤ 5.

Sue hits a ball from a height of 4 feet.  The height of the ball above the ground is a function of the horizontal distance the ball travels until it comes to rest on the ground.  Consider this complete graph of the function.

Select all values that are in the domain of the function as shown in the graph.

• -5 feet

• 0 feet

• 60 feet

• 200 feet

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

• 
• 
• 

Tags

CCSS.HSF-IF.C.7D

A student examines two graphs representing the functions f(x) = x + 5 and g(x) = x² + 5.  The student notices that the graphs both have a y-intercept at the point (0, 5).  The student makes the following claim:

“For any real number c, the y-intercepts for the graphs of y = c ∙ f(x) and y = c ∙ g(x) are the same.”

Is this true or false?

If it is TRUE, enter the y-coordinate of the y-intercept in terms of c. (0, ​ (a)   )

If its FALSE, enter the y-coordinates of the y-intercepts of  two graphs that are a counter-example. (0, ​ (b)   ) (0, ​ (c)   )

• 5
• ___

Match the following

The graphs below show different information about the weather in a large city in the U.S. for one week in May.

Determine whether each graph represents the given quantity as a function of time.

• False

• Graph A represents temperature as a function of time.

• True

• Graph B represents amount of accumulated precipitation as a function of time.

• True

• Graph C represents the solar intensity as a function of time.

Tags

CCSS.HSF.IF.A.2

Consider the function f(x) = 10x + 25.  Identify an appropriate domain for the function if it is used to model each of the following contexts.

c

b

a

X

X

X

Match the following

This graph shows the population of mice in a study, modeled as a function of time.  The study begins on day 0 and ends on day 200.  Select True or False for each statement.

• True

• The least number of mice during the study was 130.

• True

• There are two intervals of time where the mouse population decreases.

• False

• The mouse population was decreased between day 40 and day 80.

• True

• The mouse population was the greatest around day 160.

Tags

CCSS.HSF.IF.B.4

A bird flies out of its nest.  This graph represents the distance it flies from its nest (in meters) as a function of time (in seconds).

Place a X to mark the point on the graph that represents the bird’s greatest distance from its nest.

Place a O to mark the point that represents the bird’s return to its nest.

a

b

O

X

Tags

CCSS.HSF.IF.B.4