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Algebra 1 : How to graph an exponential function

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : Solving Exponential Functions

What is the horizontal asymptote of the graph of the equation $y = -2e^{x-3} -5$ ?

Possible Answers:

y=5

y=-5

$y=-\frac{5}{2}$

y=3

y=-2

Correct answer:

y=-5

Explanation:

The asymptote of this equation can be found by observing that $e^{x-3} > 0$ regardless of . We are thus solving for the value of as $e^{x-3}$ approaches zero.

$-2e^{x-3} < -2\cdot 0$

$-2e^{x-3} < 0$

$-2e^{x-3} -5 < 0-5$

$-2e^{x-3} -5 < -5$

y<-5

So the value that cannot exceed is , and the line y = -5 is the asymptote.

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Example Question #2 : Solving Exponential Functions

What is/are the asymptote(s) of the graph of the function

$f(x) = 5e^{x-2}-2$ ?

Possible Answers:

x=2

y = -2, x=-2

y = -2, x=2

y = -2

x=-2

Correct answer:

y = -2

Explanation:

An exponential equation of the form $f(x) = ae^{x-h} +k$ has only one asymptote - a horizontal one at y = k . In the given function, k = -2 , so its one and only asymptote is y = -2 .

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Example Question #1 : How To Graph An Exponential Function

$\textup{What is the \textit{x}-intercept of the equation } y=e^{x-1}-1?$

Possible Answers:

$\textup{None of the above.}$

$-\infty$

$\textup{The graph does not intercept the \textit{x}-axis.}$

Correct answer:

Explanation:

$\\ \\ \textup{Solve the equation } \\0=e^{x-1} -1\\ e^{x-1}=1\\ {x-1}=\textup{ln}(1)=0\\ x=1.\\\textup{ Remember }e^0=1 \textup{, so when plugging } x=1 \textup{ in the initial equation, you obtain }\\ e^{1-1}-1=e^0-1=1-1=0.$

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Algebra 1 : How to graph an exponential function

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Solving Exponential Functions

Example Question #2 : Solving Exponential Functions

Example Question #1 : How To Graph An Exponential Function

All Algebra 1 Resources

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