Interactive practice questions
Consider the graphs of the two exponential functions $R$R and $S$S.
A Cartesian plane has both its $x$x- and $y$y-axes extending in both directions. Two exponential functions, $R$R and $S$S, are graphed on the plane. The function $R$R is outlined in light gray, and the function $S$S is outlined in black. The horizontal asymptote of both curves is a dotted line at $y=0$y=0. The function $R$R starts near the horizontal asymptote on the left side and rises steeply upward. The function $S$S also starts near the horizontal asymptote on the left side, but it rises more gradually upward. Both curves cross the $y$y-axis at the same point, which is not marked or explicitly labeled.
One of the graphs is of $y=4^x$y=4x and the other graph is of $y=6^x$y=6x.
Which is the graph of $y=6^x$y=6x?
Graph S
Graph R
Fill in the blanks to complete the statement:
For $x<\editable{}$x<, the graph of $y=\left(\editable{}\right)^x$y=()x is below the graph of $y=\left(\editable{}\right)^x$y=()x. This is because negative values of $x$x result in fractional function values, and for any negative value of $x$x, $\left(\editable{}\right)^x$()x will result in a smaller value than $\left(\editable{}\right)^x$()x.
Consider the curve $y=4\left(2^x\right)$y=4(2x).
Consider the function $y=2-4^{-x}$y=2−4−x.