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Graphing a Shift of an Exponential Function · Physics Playground

Exercises Exponentials and logarithms

Example 2 from Algebra and Trigonometry, 6.2 Graphs of Exponential Functions

Graphing a Shift of an Exponential Function

Graph $f (x) = 2^{x + 1} - 3.$ State the domain, range, and asymptote.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We have an exponential equation of the form $f (x) = b^{x + c} + d,$ with $b = 2,$ $c = 1,$ and $d = - 3.$
Draw the horizontal asymptote $y = d$ , so draw $y = −3.$
Identify the shift as $(- c, d),$ so the shift is $(- 1, −3) .$
Shift the graph of $f (x) = b^{x}$ left 1 units and down 3 units.

Figure 7

The domain is $(- \infty, \infty);$ the range is $(- 3, \infty);$ the horizontal asymptote is $y = −3.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Graph $f (x) = 2^{x - 1} + 3.$ State domain, range, and asymptote.

How did it go?

PreviousSketching the Graph of an Exponential Function of the Form f(x) = bx Next Approximating the Solution of an Exponential Equation

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.