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Coordinate Algebra EOC (GSE) Quiz Answer KeyFunctions - (MGSE9‐12.F.IF.7e ) Exponential Functions

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

What function is shown in the graph?

A) y = -7x

B) y = 7-x

C) y = 7x – 3

D) y = 7x – 3

Explanation:Exponential graphs in standard position increase from left to right and go through the point (0, 1). This graph has been shifted down

by 3 units. The correct answer is y = 7x -3.

2) Oliver and Marie are graphing two equations on a coordinate grid. Oliver has graphed the equation y = 2x + 2.

If Marie graphs y = 2x - 3, where will the y-intercept of her graph be in relation to Oliver's graph?

A) 3 units lower

B) 5 units lower

C) 5 units higher

D) the same place

Explanation:A + 2 on the end of the equation made Oliver's y-intercept at (0, 3). The - 5 on the end of Marie's equation made her y-intercept (0,-2). Therefore, Marie's y- intercept is 5 units lower. At x = 0 the graphs will have the same value and for all x < 0, Nina's graph will

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be lower.

3) Which could be the graph of y = 3x?

A)

B)

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C)

D)

Explanation:If the base of the exponential is a whole number and is positive, the graph increases from left to right. The correct answer is A.

4) Given f(x) = abx + c. How would increasing the value of a change the graph?

A) The function would be shifted up a units

B) The function would increase at a faster rate

C) The function would decrease at a faster rate.

D) The function would be shifted to the left a units.

Explanation:

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The function would increase at a faster rate is the correct answer. Each y-value would be multiplied by a factor of a.

x

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5) Find the y-intercept of the function: f(x) = 6x + 2

A) (0, 0)

B) (0, 1)

C) (0, 2)

D) (0, 3)

Explanation:(0, 3) is correct. Plug in 0 for x to get the answer.

6)

What function is shown in the graph?

A) y = -2x

B) y = 2-x

C) y = 2x – 5

D) y = 2x – 5

Explanation:Exponential graphs in standard position increase from left to right and go through the point (0, 1). This graph has been reflected

over the x-axis. The correct answer is y = -2x.

7) Find the x-intercept of the function f(x) = ax + 1 - 1.

A) (0, 0)

B) (a, 0)

C) (-1, 0)

D) (a - 1, 0)

Explanation:

(-1, 0) is correct. Set y = 0 to get the equation 0 = ax + 1 - 1, or 1 = ax + 1. Take the natural logarithm of both sides to get 0 = (x +1)ln(a), but since ln(a) cannot equal 0, x + 1 = 0, so x = -1.

8) Graph f(x) = 2·4x - 2

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A)

B)

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C)

D)

Explanation:

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The correct answer is . The -2 moves the graph down 2and the 2 in front of the equation multiplies all the y-values by a factor of 2. Note that it passes through the origin.

9)

Which exponential function is graphed here?

A) y = 5x

B) y = 5ex

C) y = 5x + 5

D) y = 5x + 1

Explanation:

x

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y = 5x is correct. Plug in 0, 1, and 2 for x to get 1, 5, and 25 as shown.

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10)

Choose the correct formula for the function g.

A) g(x) = 2x + 3 + 2

B) g(x) = 2x + 3 - 2

C) g(x) = 2x - 3 + 2

D) g(x) = 2x - 3 - 2

Explanation:

g(x) = 2x - 3 + 2 is correct. Changing x to x - 3 shifts the graph 3 units right, and adding +2 at the end shifts it up 2 units.

11) The graphs show four exponential functions, each with equation y = abx. If a > 1 and b > 1, then which of the four could be itsgraph?

A)

B)

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C)

D)

Explanation:C is corect. Since the y-intercept, a, of the graph is greater than 1, only C can be correct. Also, since b > 1 the graph should be risingfrom left to right.

12)

What function is shown in the graph?

A) y = -4x

B) y = 4-x

C) y = 4x – 1

D) y = 4x – 1

Explanation:Exponential graphs in standard position increase from left to right and go through the point (0, 1). This graph has been shifted right

by 1 unit. The correct answer is y = 4x – 1.

13)

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Which function is graphed here?

A) y = 2x - 1

B) y = 2(x - 1)

C) y = 2x + 1

D) y = 2(x + 1)

Explanation:

y = 2x - 1 is correct. Use the points shown, (0, 0), (1, 1) to verify.

14)

Choose the correct formula for the function h.

A) h(x) = -3x - 2 - 1

B) h(x) = -3x - 2 + 1

C) h(x) = -3x + 2 - 1

x + 2

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D) h(x) = -3x + 2 + 1

Explanation:

h(x) = -3x + 2 - 1 is correct. Changing 3 to -3 reflects the graph in the x-axis, changing x to x + 2 shifts it 2 units left, and adding -1 atthe end shifts it down 1 unit.

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15)

What function is shown in the graph?

A) y = -3x

B) y = 3-x

C) y = 3x + 2

D) y = 3x + 2

Explanation:Exponential graphs in standard position increase from left to right and go through the point (0, 1). This graph has been reflected

over the y-axis. The correct answer is y = 3-x.

16)

What function is shown in the graph?

A) y = -ex

B) y = e-x

C) y = ex + 2

D) y = ex + 2

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Explanation:Exponential graphs in standard position increase from left to right and go through the point (0, 1). This graph has been shifted up by

2 units. The correct answer is y = ex + 2.

17) The typical exponential function, y = ax, has asymptote ________ and y-intercept ________.

A) y = 0; (0,a)

B) y = 0; (0,1)

C) y = a; (0,a)

D) y = a; (0,1)

Explanation:

y = 0; (0,1) is correct. The asymptote is y = 0 since the function's range is y≥0, and the y-intercept is (0,1) since a0 = 1.

18)

In the graph shown, suppose that f(x) = ax, g(x) = bx, and h(x) = cx. Choose the true statement.

A) c < a < b

B) a < c < b

C) b < c < a

D) c < b < a

Explanation:c < b < a is correct. The larger the base, the faster the graph rises from left to right.

19)

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What is the asymptote of this function?

A) x = 3

B) y = 3

C) x = 4

D) y = 4

Explanation:The asymptote occurs at y = 4.

-2x

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20) Which of the functions graphed here could be the graph of the exponential function y = ab-2x, where a > 0?

A)

B)

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C)

D)

Explanation:

C is correct. Exponential functions of the form y = bx are always positive, and since a > 0 only C can work.

21) Which exponential function grows the fastest?

A) f(x) = 5·2x

B) f(x) = 4·3x

C) f(x) = 3·4x

D) f(x) = 2·5x

Explanation:

f(x) = 2·5x

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The base of an exponential function determines how fast it is going to grow. Since 5 is the largest base, f(x) = 2·5x grows the fastest.

22)

This exponential function y = 3(2)x + 4 represents the growth of a certain species of animal in a specific area. The y-axis representsthe number of that animal present and the x-axis represents years. What can you say about the growth of the population of thespecies every year?

A) The growth rate doubles each year.

B) The growth rate triples each year.

C) The growth rate increases by 2 each year.

D) The growth rate increases by 5 each year.

Explanation:The initial population in year zero is 7, in year one the growth is 3, in year 2 the growth is 6, and in year 3 the growth is 12.Therefore, the growth rate doubles each year.

23)

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The graph shows the first quadrant portion of four exponential functions. If the equation of the BLUE curve is y = ab-x, then theequation of the GREEN curve is

A) y = ab-x

B) y = 0.5ab-x

C) y = a(0.5bx)

D) y = ab-x - 0.5

Explanation:

y = 0.5abx. Since the y-intercept of the blue curve is 1, we know a = 1. So, 0.5a = 0.5, which is the y-intercept of the green curve.

24) Jack and Nina are graphing two equations on a coordinate grid. Jack has graphed the equation y = 2x.

If Nina graphs y = 5x, where will her graph be in relation to the graph Jack made?

A) For all x > 0 the graph will be higher.

B) For all x > 0 the graph will be lower.

C) For all x the graph will be higher.

D) For all x the graph will be lower.

Explanation:Changing the 2 to a 5 makes an exponential growth function increase at a faster rate. Therefore, for all x > 0 the graph will behigher. At x = 0 the graphs will have the same value and for all x < 0, Nina's graph will be lower.

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25)

Given that f(x) = 2x, choose the correct formula for g(x).

A) g(x) = -2x

B) g(x) = (-2)x

C) g(x) = 1

2

x

D) g(x) = -1

2

x

Explanation:

g(x) = 1

2

x is correct. Since g is the reflection of f in the y-axis, we get g(x) = 2-x, or (2-1)x, which equals the answer.

26) Given f(x) = ab-x + c. How would increasing the value of a change the graph?

A) The function would increase at a faster rate

B) The function would increase at a slower rate.

C) The function would decrease at a faster rate.

D) The function would decrease at a slower rate.

Explanation:The function would decrease at a faster rate. is the correct answer. Each y-value would be multiplied by a factor of a.

27) Which could be the graph of y = 3-x?

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A)

B)

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C)

D)

Explanation:If the base of the exponential is a whole number and is positive, and the exponent is negative, the graph decreases from left toright. The correct answer is D.

28) If you subtracted 3 from the exponent in an exponential function, what would happen to the graph?

A) It would move up 3

B) It would move down 3

C) It would move to the left 3

D) It would move to the right 3

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Explanation:The correct answer is It would move to the right 3. Adding or subtracting a number in the exponent moves the graph horizontally. Apositive number moves to the left and a negative number moves to the right.

29) Find the x-intercept of the function: f(x) = 6x - 2. Round answer to the nearest hundredth, if necessary.

A) (0.39, 0)

B) (1.00, 0)

C) (2.58, 0)

D) (3.00, 0)

Explanation:

(0.39, 0) is correct. Plug in 0 for f(x) to get 0 = 6x - 2, or 2 = 6x. Take the log of both sides, or try values for x to get the answer.

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30)

The graph shows the first quadrant portion of four exponential functions. Which equation could generate the BLUE curve?

A) y = 3-x

B) y = 3-x + 1

C) y = 3-x + 2

D) y = 3-x + 3

Explanation:

y = 3-x. The y-intercept of the blue curve is 1, and only this equation allows for that.