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Hong Kong
Stage 4 - Stage 5

Exponentials VS Linear or Quadratic Functions

Interactive practice questions

A linear function and exponential function have been drawn on the same coordinate plane.

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A number plane with the axes labeled as x and y. x-axis ranges from 0 to 5 and y-axis ranges from 0 to 20. A straight line(a linear function, $ArbitraryFunction('4*x')$ArbitraryFunction(4*x)) and a curve line(an exponential function, $ArbitraryFunction('2**x')$ArbitraryFunction(2**x)) is plotted. (Do not mention the linear function and exponential function as these are not given in the image)
a

Over any $1$1 unit interval of $x$x, by what constant amount does the linear function grow?

b

Over any $1$1 unit interval of $x$x, by what constant ratio does the exponential function grow?

c

Would it be correct to state that the linear function always produces greater values than the exponential function?

Yes

A

No

B
d

As $x$x approaches infinity, which function increases more rapidly?

The linear function

A

The exponential function

B
Easy
2min

Consider the functions $f\left(x\right)=3x$f(x)=3x and $g\left(x\right)=3^x$g(x)=3x.

Easy
6min

Several points have been plotted on the number plane.

Easy
2min

Consider the following table of values for the functions for $x\ge1$x1:

$f\left(x\right)=\left(1.05\right)^x$f(x)=(1.05)x and $g\left(x\right)=5x$g(x)=5x.

Easy
1min
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