Functions (Graphs and Behaviour)

Hong Kong

Stage 4 - Stage 5

Michael is going to use the point of intersection of graphs to find an approximation to the positive solution of $\log\left(x\right)-1=-x+5$`l``o``g`(`x`)−1=−`x`+5.

a

One of the graphs is $f\left(x\right)=\log\left(x\right)-1$`f`(`x`)=`l``o``g`(`x`)−1. What function $g\left(x\right)$`g`(`x`) should the other graph be of?

b

The graph of $f\left(x\right)$`f`(`x`) has been provided. On the same set of axes, graph $g\left(x\right)=-x+5$`g`(`x`)=−`x`+5.

Loading Graph...

c

Between which two values does the solution of the equation lie? There may be more than one solution.

$x=4$`x`=4 and $x=9$`x`=9

A

$x=2$`x`=2 and $x=5$`x`=5

B

$x=6$`x`=6 and $x=7$`x`=7

C

$x=5$`x`=5 and $x=6$`x`=6

D

Easy

1min

Consider the function $f\left(x\right)=\log_2\left(x+1\right)$`f`(`x`)=`l``o``g`2(`x`+1).

Easy

1min

Consider the functions $f\left(x\right)=x^3+2x^2$`f`(`x`)=`x`3+2`x`2 and $g\left(x\right)=x+4$`g`(`x`)=`x`+4.

Medium

2min

The populations of two competing species of animals is given by $f\left(t\right)=215t+3$`f`(`t`)=215`t`+3 and $g\left(t\right)=\frac{1}{t-3}$`g`(`t`)=1`t`−3, where $f\left(t\right)$`f`(`t`) and $g\left(t\right)$`g`(`t`) represent the respective populations $t$`t` years from now. Jenny is looking to determine approximately when their populations will be equal.

Medium

4min

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