Exponentials VS Linear or Quadratic Functions
Interactive practice questions
A linear function and exponential function have been graphed on the same coordinate axes.
Over a $1$1 unit interval of $x$x, by what constant amount does the linear function grow?
Over a $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.