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10.11 Comparing exponential and quadratic functions

Lesson

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.

 

Practice questions

Question 1

Consider the functions $f\left(x\right)=9x^2$f(x)=9x2 and $g\left(x\right)=9^x$g(x)=9x.

  1. 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) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
  2. Select the graph for $f\left(x\right)$f(x).

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    D
  3. Select the graph for $g\left(x\right)$g(x).

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    D
  4. Which function has a minimum value?

    $f\left(x\right)$f(x)

    A

    $g\left(x\right)$g(x)

    B

    Both

    C

    Neither

    D
  5. Which function has a horizontal asymptote?

    $f\left(x\right)$f(x)

    A

    $g\left(x\right)$g(x)

    B

    Both

    C

    Neither

    D

Question 2

Consider the functions $f\left(x\right)=2x^2-6$f(x)=2x26 and $g\left(x\right)=2^x-6$g(x)=2x6.

  1. 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) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
  2. Select the graph for $f\left(x\right)$f(x).

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    D
  3. Select the graph for $g\left(x\right)$g(x).

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    D
  4. Which function is increasing when $x<0$x<0?

    $f\left(x\right)$f(x)

    A

    $g\left(x\right)$g(x)

    B

    Both

    C

    Neither

    D
  5. Which function is increasing when $x>0$x>0?

    $f\left(x\right)$f(x)

    A

    $g\left(x\right)$g(x)

    B

    Both

    C

    Neither

    D

Question 3

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)=6x8.

  1. 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) $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
  2. Select the graph for $f\left(x\right)$f(x).

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    D
  3. Select the graph for $g\left(x\right)$g(x).

    Loading Graph...

    A

    Loading Graph...

    B

    Loading Graph...

    C

    Loading Graph...

    D
  4. Which function has a minimum value?

    $f\left(x\right)$f(x)

    A

    $g\left(x\right)$g(x)

    B

    Both

    C

    Neither

    D
  5. Which function has a horizontal asymptote?

    $f\left(x\right)$f(x)

    A

    $g\left(x\right)$g(x)

    B

    Both

    C

    Neither

    D

Outcomes

A1:F-LE.A.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

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