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Evaluating Functions


We've seen the form "$y=$y=" when we learnt about graphing. We've used this form to describe straight lines, parabolas and hyperbolas just to name a few.

In Is this a Functional Relationship, we were also introduced to the concept of functions. Where each input yielded a unique output.

When we are writing in function notation, instead of writing "$y=$y=", we write "$f(x)=$f(x)=". This gives us a bit more flexibility when we're working with equations or graphing as we don't have to keep track of so many $y$ys! Instead, using function notation, we can write $f(x)=$f(x)=, $g(x)=$g(x)=, $h(x)=$h(x)= and so on. These are all different expressions that involve only $x$x as the variable.

We can also evaluate "$f(x)$f(x)" by substituting values into the equations just like we would if the question was in the form "$y=$y=".


Question 1

If $A(x)=x^2+1$A(x)=x2+1 and $Q(x)=x^2+9x$Q(x)=x2+9x, find:

A) $A(5)$A(5)

Think: This means we need to substitute $5$5 in for $x$x in the $A(x)$A(x) equation.


$A(5)$A(5)  $=$= $5^2+1$52+1
  $=$= $26$26


B) $Q(6)$Q(6)

Think: This means we need to substitute $6$6 in for $x$x in the $Q(x)$Q(x) equation.


$Q(6)$Q(6) $=$= $6^2+9\times6$62+9×6
  $=$= $36+54$36+54
  $=$= $90$90


C) $A(10)+Q(7)$A(10)+Q(7)

Think: This question will use both equations.


Let's work it out separately first:

$A(10)$A(10) $=$= $10^2+1$102+1
  $=$= $101$101
$Q(7)$Q(7) $=$= $7^2+9\times7$72+9×7 
  $=$= $112$112
$101+112$101+112 $=$= $213$213


We can also do this as one long calculation:

$10^2+1+7^2+9\times7$102+1+72+9×7 $=$=  $101+112$101+112
  $=$= $213$213


Question 2

Consider the function $f\left(x\right)=8x+6$f(x)=8x+6.

  1. Determine the output produced by the input value $x=5$x=5.

Question 3

If $Z(y)=y^2+12y+32$Z(y)=y2+12y+32, find $y$y when $Z(y)=-3$Z(y)=3.

  1. Write both solutions on the same line separated by a comma.


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