Exponential functions have the form $A\left(a^x\right)+k$A(ax)+k. Quadratic functions have the form $ax^2+bx+c$ax2+bx+c. Here are some features of both functions.
Exponential functions | Quadratic functions | |
---|---|---|
$x$x-intercepts | Either zero or one $x$x-intercept | Either zero, one or two $x$x-intercepts |
$y$y-intercept | One $y$y-intercept | One $y$y-intercept |
Asymptotes | One horizontal asymptote | No asymptotes |
Turning points | No turning points | One turning point |
Direction | Either always increasing or always decreasing | Increasing on one side of the turning point and decreasing on the other. |
Consider the functions $f\left(x\right)=9x^2$f(x)=9x2 and $g\left(x\right)=9^x$g(x)=9x.
Complete the table of values.
$x$x | $-2$−2 | $-1$−1 | $0$0 | $1$1 | $2$2 |
---|---|---|---|---|---|
$f\left(x\right)$f(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
$g\left(x\right)$g(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
Select the graph for $f\left(x\right)$f(x).
Select the graph for $g\left(x\right)$g(x).
Which function has a minimum value?
$f\left(x\right)$f(x)
$g\left(x\right)$g(x)
Both
Neither
Which function has a horizontal asymptote?
$f\left(x\right)$f(x)
$g\left(x\right)$g(x)
Both
Neither
Consider the functions $f\left(x\right)=2x^2-6$f(x)=2x2−6 and $g\left(x\right)=2^x-6$g(x)=2x−6.
Complete the table of values.
$x$x | $-2$−2 | $-1$−1 | $0$0 | $1$1 | $2$2 |
---|---|---|---|---|---|
$f\left(x\right)$f(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
$g\left(x\right)$g(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
Select the graph for $f\left(x\right)$f(x).
Select the graph for $g\left(x\right)$g(x).
Which function is increasing when $x<0$x<0?
$f\left(x\right)$f(x)
$g\left(x\right)$g(x)
Both
Neither
Which function is increasing when $x>0$x>0?
$f\left(x\right)$f(x)
$g\left(x\right)$g(x)
Both
Neither
Consider the functions $f\left(x\right)=x^2+2x+5$f(x)=x2+2x+5 and $g\left(x\right)=6^x-8$g(x)=6x−8.
Complete the table of values.
$x$x | $-2$−2 | $-1$−1 | $0$0 | $1$1 | $2$2 |
---|---|---|---|---|---|
$f\left(x\right)$f(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
$g\left(x\right)$g(x) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
Select the graph for $f\left(x\right)$f(x).
Select the graph for $g\left(x\right)$g(x).
Which function has a minimum value?
$f\left(x\right)$f(x)
$g\left(x\right)$g(x)
Both
Neither
Which function has a horizontal asymptote?
$f\left(x\right)$f(x)
$g\left(x\right)$g(x)
Both
Neither