Functions (Graphs and Behaviour)

Hong Kong

Stage 4 - Stage 5

Consider the following linear equations:

$y=5x-7$`y`=5`x`−7 and $y=-x+5$`y`=−`x`+5

a

Plot the lines of the two equations on the same graph.

Loading Graph...

b

State the values of $x$`x` and $y$`y` which satisfy both equations.

$x$`x` = $\editable{}$

$y$`y` = $\editable{}$

Easy

Approx 2 minutes

Consider the functions $f\left(x\right)=-3\left(x^2-3\right)$`f`(`x`)=−3(`x`2−3) and $g\left(x\right)=-6x$`g`(`x`)=−6`x`.

Below is the graph of $y=-x^2-2x+3$`y`=−`x`2−2`x`+3.

We want to solve the equation $x^2-x-2=0$`x`2−`x`−2=0 graphically by finding the point of intersection of $y=-x^2-2x+3$`y`=−`x`2−2`x`+3 and a straight line graph.

Consider the functions $f\left(x\right)=5x+5$`f`(`x`)=5`x`+5 and $g\left(x\right)=2^x+5$`g`(`x`)=2`x`+5.

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