# Lesson Worksheet: Natural Exponential Functions Mathematics

In this worksheet, we will practice identifying, writing, evaluating, sketching, and analyzing natural exponential functions and their transformations.

Q1:

Let . Find .

Q2:

Q3:

Find the intercepts and asymptotes of the graph of the function .

• A-intercept: 0, -intercept: , asymptote:
• B-intercept: , -intercept: 0, asymptote:
• C-intercept: , -intercept: 0, asymptote:
• D-intercept: 0, -intercept: 0, asymptote:
• E-intercept: 0, -intercept: , asymptote:

Q4:

Given that , find .

• A
• B
• C
• D
• E

Q5:

The diagram shows the graph of a function of the form for constants , , and . Find the values of and and the sign of .

• A, , and is negative.
• B, , and is positive.
• C, , and is positive.
• D, , and is positive.
• E, , and is negative.

Q6:

The diagram shows the graph of a function of the form for constants , , and . Find the values of and and the sign of .

• A, , and is negative.
• B, , and is positive.
• C, , and is negative.
• D, , and is positive.
• E, , and is negative.

Q7:

Which of the following is a possible graph of ?

• A • B • C • D Q8:

Which of the following is a possible graph of ?

• A • B • C • D Q9:

Differentiate with respect to .

• A
• B
• C
• D
• E

Q10:

Find the point on the curve where the tangent line has a slope of .

• A
• B
• C
• D
• E