Interactive practice questions
A linear function and exponential function have been drawn on the same coordinate plane.
A Coordinate plane has its x-axis ranging from $0$0 to $5$5 and its y-axis ranging from $0$0 to $20$20. A linear function is plotted as a gray line on the Coordinate plane. The line starts at $\left(0,0\right)$(0,0) and moves upward to the right. The line passes through the point $\left(1,4\right)$(1,4) and extends beyond the visible part of the graph. An exponential function is plotted as a black curve on the same Coordinate plane. The curve starts at $\left(0,1\right)$(0,1) and moves upward to the right. The curve passes through the point $\left(1,2\right)$(1,2) and extends beyond the visible part of the graph. The points are not marked and the coordinates are not explicitly labeled or given.
Over any $1$1 unit interval of $x$x, by what constant amount does the linear function grow?
Over any $1$1 unit interval of $x$x, by what constant ratio does the exponential function grow?
Would it be correct to state that the linear function always produces greater values than the exponential function?
Yes
No
As $x$x approaches infinity, which function increases more rapidly?
The linear function
The exponential function
Consider the functions $f\left(x\right)=3x$f(x)=3x and $g\left(x\right)=3^x$g(x)=3x.
Several points have been plotted on the number plane.
Consider the following table of values for the functions for $x\ge1$x≥1:
$f\left(x\right)=\left(1.05\right)^x$f(x)=(1.05)x and $g\left(x\right)=5x$g(x)=5x.