Exponential and Logarithm Functions

Is this exponential growth or decay?

• Growth

• Decay

Tags

CCSS.HSF-IF.C.8B

Which function is often called 'the' exponential function?

• f(x) = 2^x

• f(x) = 10^x

• f(x) = e^x

• f(x) = 5^x

For the function f(x) = log_a(x) where a > 1, what is the value of f(1)?

• 2

• 1

• 0

• 3

What is the general shape of the graph of the function f(x) = a^x when a > 1?

• Close to the x-axis for negative x and increases rapidly for positive x

• Close to the y-axis for positive x and increases rapidly for decreasing negative x

• Close to the y-axis for negative x and increases slowly for positive x

• Close to the x-axis for positive x and increases slowly for negative x

Tags

CCSS.HSF-IF.C.7E

For the function f(x) = log_a(x) where a > 1, what is the effect of varying a?

• Close to the negative y-axis for x < 1 and increases slowly for positive x

• Close to the x-axis for positive x and increases rapidly for decreasing negative x

• Close to the y-axis for positive x and increases rapidly for negative x

• Close to the x-axis for negative x and increases rapidly for positive x

Tags

CCSS.HSF-IF.C.7E

What is the relationship between the exponential function f(x) = e^x and the logarithm function f(x) = ln(x)?

• Reflection in the y-axis

• Reflection in the line y = -x

• Reflection in the y = x line

• Reflection in the x-axis

Tags

CCSS.HSF.BF.B.5

For the function f(x) = log_a(x) where a < 1, what is the general shape of the graph?

• Close to the x-axis for negative x and increases rapidly for positive x

• Close to the y-axis for negative x and increases rapidly for positive x

• Close to the x-axis for positive x and increases rapidly for decreasing negative x

• Close to the positive y-axis for x < 1 and decreases slowly for positive x

Tags

CCSS.HSF-IF.C.7E

Which of the following is true about the graph of f(x) = (1/a)^x?

• Reflection in the y-axis of f(x) = a^x

• Reflection in the x-axis of f(x) = a^x

• Reflection in the line y = x of f(x) = a^x

• Reflection in the line y = -x of f(x) = a^x

Tags

CCSS.HSF.BF.B.3

What is the important property of the graph of f(x) = log_a(x) for any value of a?

• Always passes through the point (0, 1)

• Always passes through the point (1, 0)

• Always passes through the point (-1, 0)

• Always passes through the point (0, -1)

Tags

CCSS.HSF-IF.C.7E

What is the effect of varying a in the function f(x) = a^x when 0 < a < 1?

• Close to the x-axis for positive x and increases rapidly for decreasing negative x

• Close to the y-axis for positive x and increases rapidly for negative x

• Close to the y-axis for negative x and increases rapidly for positive x

• Close to the x-axis for negative x and increases rapidly for positive x

Tags

CCSS.HSF-IF.C.7E