Alg 462 Quiz Graphs Exponential (e) and Logarithmic

Answer each question showing all your work. Watch your time so you are not stuck in the middle of a question when it is submitted.

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2

Simplify the expression using the properties of exponents. Show all your work. (2 points)

3

Simplify the expression using the properties of exponents. Show all your work. (3 points)

3

Simplify the expression using the properties of exponents. Show all your work. (3 points)

2

Tell whether the function is an example of exponential growth or exponential decay (1 point). Briefly explain how you know in the show your work section (1 more point).

3

Write a new exponential function g(x) with base e and parent function f(x) = ex that represents the indicated transformations. (3 points)

“a translation one unit to the left, reflection across the x-axis, and down three units”

3

Write a new exponential function h(x) with base e and parent function f(x) = ex that represents the indicated transformations. (3 points)

“a translation four units right; vertical shrink by a factor of 1/3, and a translation six units up”

2

Describe the transformations for the function. (2 points)

3

Describe the transformations for the function. (3 points)

3

Graph the function by filling in the table. Use a calculator. (3 points)

1

What is the range? (1 point)

1

Rewrite the logarithmic equation into an exponential equation. (1 point)

1

Rewrite the logarithmic equation into an exponential equation. (1 point)

1

Rewrite the exponential equation into a logarithmic equation. (1 point)

1

Rewrite the exponential equation into a logarithmic equation. (1 point)

2

Evaluate the logarithm without using a calculator. (2 points)

2

Evaluate the logarithm without using a calculator. (2 points)

2

Evaluate the logarithm without using a calculator. (2 points)

1

Evaluate the logarithm without using a calculator. (2 points)

3

Write a new logarithmic function h(x) from the parent function f(x) = log2x that represents the indicated transformations. (3 points)

“a translation 4 units right; reflection across the x-axis; and a translation down 5 units”

4

Describe the transformations for the logarithmic function. (4 points)

3

Graph the function. (3 points)

1

State the domain. (1 point)

1

State the x-intercept. Write your answer as an ordered pair (x ,y). (2 points)

2

(2 points)

2

Simplify the expression using the properties of exponents. Show all your work. (2 points)

Simplify the expression using the properties of exponents. Show all your work. (3 points)

Simplify the expression using the properties of exponents. Show all your work. (3 points)

Tell whether the function is an example of exponential growth or exponential decay (1 point). Briefly explain how you know in the show your work section (1 more point).

Write a new exponential function g(x) with base e and parent function f(x) = ex that represents the indicated transformations. (3 points)“a translation one unit to the left, reflection across the x-axis, and down three units”

Write a new exponential function h(x) with base e and parent function f(x) = ex that represents the indicated transformations. (3 points)“a translation four units right; vertical shrink by a factor of 1/3, and a translation six units up”

Describe the transformations for the function. (2 points)

Describe the transformations for the function. (3 points)

Graph the function by filling in the table. Use a calculator. (3 points)

What is the range? (1 point)

Rewrite the logarithmic equation into an exponential equation. (1 point)

Rewrite the logarithmic equation into an exponential equation. (1 point)

Rewrite the exponential equation into a logarithmic equation. (1 point)

Rewrite the exponential equation into a logarithmic equation. (1 point)

Evaluate the logarithm without using a calculator. (2 points)

Evaluate the logarithm without using a calculator. (2 points)

Evaluate the logarithm without using a calculator. (2 points)

Evaluate the logarithm without using a calculator. (2 points)

Write a new logarithmic function h(x) from the parent function f(x) = log2x that represents the indicated transformations. (3 points)“a translation 4 units right; reflection across the x-axis; and a translation down 5 units”

Describe the transformations for the logarithmic function. (4 points)

Graph the function. (3 points)

State the domain. (1 point)

State the x-intercept. Write your answer as an ordered pair (x ,y). (2 points)

(2 points)

BONUS: Order the logarithms least to greatest without a calculator...Use estimating!

Write a new exponential function g(x) with base e and parent function f(x) = ex that represents the indicated transformations. (3 points)

“a translation one unit to the left, reflection across the x-axis, and down three units”

Write a new exponential function h(x) with base e and parent function f(x) = ex that represents the indicated transformations. (3 points)

“a translation four units right; vertical shrink by a factor of 1/3, and a translation six units up”

Write a new logarithmic function h(x) from the parent function f(x) = log2x that represents the indicated transformations. (3 points)

“a translation 4 units right; reflection across the x-axis; and a translation down 5 units”