What is the asymptote of y=e^x?

The x-axis, y=0, as x\to-\infty.

How is the graph of y=e^{-x} related to y=e^x?

It is a reflection in the y-axis.

What transformation takes y=e^x to y=e^{x+2}?

A translation of \begin{pmatrix}-2\\ 0\end{pmatrix}.

x=\frac{\ln p-b}{a}, provided p0.

Simplify \ln(e^{x}) and e^{\ln x}.

Both equal x (for e^{\ln x}, x0).

The exponential function e^xEdexcel International A Level Maths: Flashcards

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State the range of $y=e^x$.

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State the range of $y=e^x$ .: $y>0$ .
What are the coordinates of the $y$ -intercept of $y=e^x$ ?: $(0,1)$ .
What is the asymptote of $y=e^x$ ?: The $x$ -axis, $y=0$ , as $x\to-\infty$ .
How is the graph of $y=e^{-x}$ related to $y=e^x$ ?: It is a reflection in the $y$ -axis.
What is the horizontal asymptote of $y=e^{ax+b}+c$ ?: $y=c$ .
What is the range of $y=e^{ax+b}+c$ when $a\ne0$ ?: $y>c$ .
Find the $y$ -intercept of $y=e^{ax+b}+c$ .: $(0,\,e^{b}+c)$ .
What transformation takes $y=e^x$ to $y=e^{x+2}$ ?: A translation of $\begin{pmatrix}-2\\ 0\end{pmatrix}$ .
Solve $e^{ax+b}=p$ .: $x=\frac{\ln p-b}{a}$ , provided $p>0$ .
Simplify $\ln(e^{x})$ and $e^{\ln x}$ .: Both equal $x$ (for $e^{\ln x}$ , $x>0$ ).
Why has $e^{x}=-3$ no solution?: $e^x>0$ for all real $x$ .
What does $A$ represent in $y=Ae^{kt}$ ?: The value of $y$ when $t=0$ .
Solve $e^{2x}=7$ exactly.: $x=\frac12\ln7$ .

Exam questions on The exponential function e^x

The function $f$ is defined by $f(x)=e^{2x-1}+3$ for all real $x$ .
Write down the range of $f$ and give a reason why $f(x)$ can never equal $3$ .2 marks
The mass $M$ grams of a radioactive sample is modelled by $M=80e^{-0.05t}$ , where $t$ is the time in hours after the sample was first measured.
Find the time at which the mass of the sample is $20$ g. Give your answer in hours to 3 significant figures.2 marks
The curve $C$ has equation $y=e^{3x}-5$ and the line $l$ has equation $y=20$ .
Find the exact coordinates of the points where $C$ crosses the coordinate axes.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).