Answers Academy - Algebra Functions and Data AnalysisUnit Test

Unit Test Answers

25 verified answers

A factory produces 1,250,000 toys each year. The number of toys is expected to increase by about 150% per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

n = 1.5 t squared + 1.25

n = 1.5 t + 1.25

n = 1.25 times 2.5 Superscript t

Free Preview

The range of which function is ?

y = 2x

y = 2(5x)

y = 5x +2

y = 5x + 2

Which of the following shows the graph of y = 4x + 3?

On a coordinate plane, an exponential function starts at y = 3 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly in quadrant 2.

On a coordinate plane, an exponential function starts at y = 0 in quadrant 2 and then increases rapidly into quadrant 1.

On a coordinate plane, an exponential function starts at y = negative 3 in quadrant 3 and then increases rapidly into quadrant 1.

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

y = x cubed minus 4

y = (x minus 4) cubed

y = (negative x minus 4) cubed

y = (negative x) cubed minus 4

Which is the graph of ?

On a coordinate plane, a curve starts at y = negative 3 and curves up into quadrant 1. It approaches y = 3.

On a coordinate plane, a curve starts at y = negative 2 and curves up into quadrant 2. It approaches y = 2 in quadrant 2.

On a coordinate plane, a curve starts at y = 3 and curves down into quadrant 4. It approaches y = negative 3 in quadrant 4.

On a coordinate plane, a curve starts at y = 4 and curves down into quadrant 3. It approaches y = negative 3 in quadrant 3.

Which of the following is true about the base b of a logarithmic function?

b > 0 and b = 1

b > 0 and

b < 0 and

b < 0 and b = 1

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

y = 9 (x + one-half) squared minus thirteen-fourths

y = 9 (x + one-half) squared minus 1

y = 9 (x + one-half) squared + five-fourths

y = 9 (x + one-half) squared minus five-fourths

Which equation has a graph that lies entirely above the x-axis?

y = –(x + 7)2 + 7

y = (x – 7)2 – 7

y = (x – 7)2 + 7

y = (x – 7)2

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue = price number of backpacks.)

$9.00 per backpack gives the maximum revenue; the maximum revenue is $32.00.

$12.00 per backpack gives the maximum revenue; the maximum revenue is $312.00.

$12.50 per backpack gives the maximum revenue; the maximum revenue is $312.50.

$15.00 per backpack gives the maximum revenue; the maximum revenue is $20.00.

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?

reciprocal

square root

exponential

quadratic

Which graph represents an exponential decay function?

On a coordinate plane, a curve opens up and to the right in quadrant 4.

On a coordinate plane, a curve opens up and to the right in quadrants 1 and 2. The line rapidly decreases in quadrant 2 and then curves and approaches the x-axis in quadrant 1.

On a coordinate plane, a line slightly curves up in quadrant 1.

On a coordinate plane, a line slowly increases in quadrant 2 and then increases rapidly into quadrant 1.

What is the domain of ?

all real numbers less than –3

all real numbers greater than –3

all real numbers less than 3

all real numbers greater than 3

Based on the family the graph below belongs to, which equation could represent the graph?

y = StartFraction 1 Over x + 2 EndFraction + 3

y = 0.2 Superscript x Baseline + 3

y = x cubed + 3

y = log x + 3

If you are given the graph of , how could you graph ?

Translate each point of the graph of h(x) 3 units up.

Translate each point of the graph of h(x) 3 units down.

Translate each point of the graph of h(x) 3 units right.

Translate each point of the graph of h(x) 3 units left.

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. What is the maximum height the rocket reaches?

16 ft

36 ft

48 ft

144 ft

How is the graph of transformed to produce the graph of ?

The graph is translated left 5 units, compressed vertically by a factor of , and translated up 3 units.

The graph is stretched vertically by a factor of , translated left 5 units, and translated up 3 units.

The graph is translated left 5 units, compressed horizontally by a factor of , and translated down 3 units.

The graph is stretched horizontally by a factor of , translated left 5 units, and translated down 3 units.

Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?

6 units left and 9 units down

6 units right and 9 units down

6 units left and 9 units up

6 units right and 9 units up

Which equation represents a graph with a vertex at (–3, 2)?

y = 4x2 + 24x + 38

y = 4x2 – 24x + 38

y = 4x2 + 12x + 2

y = 4x2 + 16x + 13

The graph below represents c, the amount a phone company charges, based on m, the number of minutes the customer uses each month. If there are a maximum of 44,640 minutes in a month, which equation best represents the phone company’s monthly charges?