6.01 Characteristics of exponential functions
Interactive practice questions
Consider the graph of the equation $y=4^x$y=4x.
What can we say about the $y$y-value of every point on the graph?
The $y$y-value of most points of the graph is greater than $1$1.
The $y$y-value of every point on the graph is positive.
The $y$y-value of every point on the graph is an integer.
The $y$y-value of most points on the graph is positive, and the $y$y-value at one point is $0$0.
As the value of $x$x gets large in the negative direction, what do the values of $y$y approach but never quite reach?
$4$4
$-4$−4
$0$0
What do we call the horizontal line $y=0$y=0, which $y=4^x$y=4x gets closer and closer to but never intersects?
A horizontal asymptote of the curve.
An $x$x-intercept of the curve.
A $y$y-intercept of the curve.
Consider the function $y=3^x$y=3x.
Consider the function $y=3^{-x}$y=3−x.
If the graph of $y=2^x$y=2x is moved down by $7$7 units, what is its new equation?