Lesson Worksheet: Natural Exponential Functions Mathematics

Start Practising

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

Q1:

Let 𝑓(𝑥)=𝑒. Find 𝑓(6).

Q2:

Let 𝑓(𝑥)=2𝑒+5. Find 𝑓(4). Round your answer to four decimal places.

Q3:

Find the intercepts and asymptotes of the graph of the function 𝑓(𝑥)=2𝑒−2.

  • A𝑥-intercept: 0, 𝑦-intercept: −2, asymptote: 𝑦=−2
  • B𝑥-intercept: −2, 𝑦-intercept: 0, asymptote: 𝑦=0
  • C𝑥-intercept: −2, 𝑦-intercept: 0, asymptote: 𝑦=−2
  • D𝑥-intercept: 0, 𝑦-intercept: 0, asymptote: 𝑦=−2
  • E𝑥-intercept: 0, 𝑦-intercept: −2, asymptote: 𝑦=0

Q4:

Given that 𝑓(𝑥)=𝑒, find 𝑓(𝑥+2).

  • A𝑒
  • B𝑒
  • C𝑒
  • D𝑒
  • E𝑒

Q5:

The diagram shows the graph of a function of the form 𝑓(𝑥)=𝑎𝑒+𝑐 for constants 𝑎, 𝑏, and 𝑐.

Find the values of 𝑎 and 𝑐 and the sign of 𝑏.

  • A𝑎=−2, 𝑐=−3, and 𝑏 is negative.
  • B𝑎=−3, 𝑐=−2, and 𝑏 is positive.
  • C𝑎=−3, 𝑐=2, and 𝑏 is positive.
  • D𝑎=−2, 𝑐=3, and 𝑏 is positive.
  • E𝑎=−2, 𝑐=3, and 𝑏 is negative.

Q6:

The diagram shows the graph of a function of the form 𝑓(𝑥)=𝑎𝑒+𝑐 for constants 𝑎, 𝑏, and 𝑐.

Find the values of 𝑎 and 𝑐 and the sign of 𝑏.

  • A𝑎=−2, 𝑐=−1, and 𝑏 is negative.
  • B𝑎=−1, 𝑐=−2, and 𝑏 is positive.
  • C𝑎=2, 𝑐=−1, and 𝑏 is negative.
  • D𝑎=1, 𝑐=−2, and 𝑏 is positive.
  • E𝑎=1, 𝑐=−2, and 𝑏 is negative.

Q7:

Which of the following is a possible graph of 𝑦=𝑒−1?

  • A
  • B
  • C
  • D

Q8:

Which of the following is a possible graph of 𝑦=−𝑒+3?

  • A
  • B
  • C
  • D

Q9:

Differentiate 6𝑒 with respect to 𝑥.

  • A23𝑒
  • B4𝑒
  • C4𝑒
  • D32𝑒
  • E4𝑒

Q10:

Find the point on the curve 𝑦=𝑒+1 where the tangent line has a slope of −2.

  • A(2,0)
  • B(1,2)
  • C(−2,0)
  • D(0,−2)
  • E(0,2)

Practice Means Progress

Boost your grades with free daily practice questions. Download Nagwa Practice today!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.