The graphs of the functions $f(x)$ and $h(x)$ are shown on the co-ordinate grid on the right. The functions are: $f(x) = x + 1$ $h(x) = x^2 - 3x - 1$. (a) Match the functions to the graphs by writing $f(x)$ or $h(x)$ in the box next to the corresponding graph. (b) For one of the functions above, give a reason for your answer in part (a). Function: Reason for your answer: (c) Use the graphs to estimate the solution of the equation $x + 1 = x^2 - 3x - 1$, between -1 and 4. $x = $ (d) Work out the value of $h(8)$. Remember that $h(x) = x^2 - 3x - 1$.

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The graphs of the functions $f(x)$ and $h(x)$ are shown on the co-ordinate grid on the right - Junior Cycle Mathematics - Question 13 - 2016

Question 13

The graphs of the functions $f(x)$ and $h(x)$ are shown on the co-ordinate grid on the right. The functions are: $f(x) = x + 1$ $h(x) = x^2 - 3x - 1$. (a) Match ... show full transcript

Worked Solution & Example Answer:The graphs of the functions $f(x)$ and $h(x)$ are shown on the co-ordinate grid on the right - Junior Cycle Mathematics - Question 13 - 2016

Step 1

Match the functions to the graphs

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Answer

The function $f(x)$ is the straight line, whereas the function $h(x)$ is the curve as it represents a quadratic function. The line corresponds to $f(x)$ .

Step 2

For one of the functions above, give a reason for your answer in part (a)

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Answer

Function: $f(x)$

Reason for your answer: $f(x)$ is linear, and it has no $x^2$ term, indicating a straight-line graph.

Step 3

Use the graphs to estimate the solution of the equation $x + 1 = x^2 - 3x - 1$, between -1 and 4

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Answer

$x = 0$

Step 4

Work out the value of $h(8)$

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Answer

$h(8) = 8^2 - 3(8) - 1 = 64 - 24 - 1 = 39$

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