Topic 1 - Linear Functions and Systems

Benito embroiders and sells T-shirts. The graph

shows his profit as a function of the number

of shirts sold. After selling a certain number of

shirts, Benito uses some earnings to buy more

materials and then increases the price of the

shirts. Which of the following is true?

• Benito increases the price after selling

  50 shirts.

• The y -intercept represents the cost of

  one T-shirt.

• The x -intercept represents the shirts he has to sell before making a profit.

• The domain of the function is

  { x | x is a real number greater than or equal to 0}.

Tags

CCSS.HSF.IF.B.4

The graph of the function f(x) = −16x² + 10 shown

at the right represents the distance, in feet, between

a diver and th surface of the water, where x is the

number of seconds after the diver leaves the diving

board. What is the height of the diving board?

Mathematical Equivalence

ON

Which of the following correctly compares the two

parts of the function, over the intervals [0, 7]

and [8, 11] ?

• Benito made an extra $25 after selling 7 shirts.

• Benito spent $1 after selling 50 shirts.

• Benito’s profit per shirt decreases from $50 to $25.

• Benito’s profit per shirt increases from $10 to $15.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Identify the intervals on which the function is increasing

and on which the function is decreasing.

Intervals on which the function increases: (−∞, ​​​ ​​ (a)   )

Intervals on which the function decreases: (​​​ (b)   , ∞)

• −∞
• 4
• 1
• ∞

Select all the transformations of f(x) = x² that combine to

result in the graph of function g at the right.

• translation of 1 unit left

• translation of 2 units down

• horizontal stretch by a factor of 2

• vertical stretch by a factor of 2

• reflection across the x -axis

What is the equation for g , which is f(x) = 2x² + 3x − 1

reflected across the y -axis?

• g(x) = 2x² + 3x − 1

• g(x) = −2x² − 3x + 1

• g(x) = 2x² − 3x − 1

• g(x) = −2x² − 3x − 1

A bucket has a leak that started 6 hours ago. At time 0, when the bucket just

emptied, a tap was turned on for 3 hours. The amount of water in the bucket

can be modeled by the function f(x) = |x| over the interval [−6, 3] , where x is

the time, in hours, and y is the amount of water in the bucket, in gallons. A

similarly full bucket started to leak only 3 hours ago. Which translation of the

graph represents the amount of water in the second bucket if it is moved under

the tap as soon as it empties?

• g(x) = |x| + 3

• g(x) = |x + 3|

• g(x) = |x| − 3

• g(x) = |x − 3|

The graph of the function f is shown. The domain

of f is [0, 50] . What is the range of g(x) = 4f(x) ?

• [0, 50]

• [0, 70]

• [0, 1.75]

• [0, 7]

Which rule defines the function in the graph?

• 
• 
• 
• 

Tags

CCSS.HSF-IF.C.7B

A scuba diver returning to the surface swims to move up quickly, then waits a few meters below the surface to avoid pressure issues. They complete the ascent more slowly. The function f represents the diver’s height above sea level over time, in seconds. Which of the following is true for f ?

• The domain is the set of

  times −9 < x < −2 , −2 < x < 1 ,

  and 1 < x < 7 .

• The domain is the depth

  interval (−26, 1) .

• The domain is the time interval (−9, 7) .

• The domain is the depth

  interval (−9, 1] .

Tags

CCSS.HSF-IF.C.7B