6.17 Transformations of exponential functions
Interactive practice questions
Consider the original graph $y=3^x$y=3x. The function values of the graph are multiplied by $2$2 to form a new graph.
For each point on the original graph, find the point on the new graph.
| Point on original graph | Point on new graph |
| $\left(-1,\frac{1}{3}\right)$(−1,13) | $\left(-1,\editable{}\right)$(−1,) |
| $\left(0,1\right)$(0,1) | $\left(0,\editable{}\right)$(0,) |
| $\left(1,3\right)$(1,3) | $\left(1,\editable{}\right)$(1,) |
| $\left(2,9\right)$(2,9) | $\left(2,\editable{}\right)$(2,) |
What is the equation of the new graph?
Which of the following shows the correct graphs of $y=3^x$y=3x and $y=2\left(3^x\right)$y=2(3x) on the same coordinate plane?
Select the two correct statements.
For negative $x$x values, $2\left(3^x\right)$2(3x) is above $3^x$3x.
For positive $x$x values, $2\left(3^x\right)$2(3x) is below $3^x$3x.
For negative $x$x values, $2\left(3^x\right)$2(3x) is below $3^x$3x.
For positive $x$x values, $2\left(3^x\right)$2(3x) is above $3^x$3x.
If the graph of $y=2^x$y=2x is moved down by $7$7 units, what is its new equation?
This is a graph of $y=3^x$y=3x.
Consider a graph of $y=3^x$y=3x.