Functions (Graphs and Behaviour)

Hong Kong

Stage 4 - Stage 5

Lesson

As we've just seen, there are plenty of technologies we can use to help us solve more complicated equations.

Let's try the following example.

Two functions are given by $f\left(x\right)=3^x+1$`f`(`x`)=3`x`+1 and $g\left(x\right)=\left|x-2\right|$`g`(`x`)=|`x`−2|

Use technology to solve $3^x+1=\left|x-2\right|$3`x`+1=|`x`−2|

I'm going to use the Casio Classpad II to solve this, but you should use what you're most comfortable with and then check you can get the same answer.

First I enter the two functions I want to graph.

Then I change the settings of the graph so I'll get a nice picture. Sometimes you need to play around with these settings until you can see everything you need. This comes with experience, and the better you know all your various functions, the easier this becomes.

I'll now press graph and take a look at what I can see.

I'll go through my menus and select Intersection

And finally I see the solution, given as the coordinate $0,2$0,2

So my answer is $x=0$`x`=0

Consider the system of equations $\left(x-3\right)^2+\left(y-1\right)^2=16$(`x`−3)2+(`y`−1)2=16 and $y=x+2$`y`=`x`+2.

Graph both equations together on the same coordinate plane.

Loading Graph...Hence, write down the solution set for the system by finding the points of intersection.

Write all coordinate points on the same line, separated by a comma.

By graphing $y=2x-5$`y`=2`x`−5 and $y=\left|x-4\right|$`y`=|`x`−4| on a graphing calculator or otherwise, find the solution(s) of the equation $2x-5=\left|x-4\right|$2`x`−5=|`x`−4|.

By graphing $y=3x-2$`y`=3`x`−2 and $y=5x^3+2x^2-x-6$`y`=5`x`3+2`x`2−`x`−6 on a graphing calculator or otherwise, find the solution(s) of the equation $3x-2=5x^3+2x^2-x-6$3`x`−2=5`x`3+2`x`2−`x`−6.

Give your answer correct to two decimal places.