(a)
The graph of the function $y = f(x)$ is shown on the co-ordinate diagram below,
for $-3 \leq x \leq 3$, $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 10 - 2016
Question 10
(a)
The graph of the function $y = f(x)$ is shown on the co-ordinate diagram below,
for $-3 \leq x \leq 3$, $x \in \mathbb{R}$. The graph is made up of two line segm... show full transcript
Worked Solution & Example Answer:(a)
The graph of the function $y = f(x)$ is shown on the co-ordinate diagram below,
for $-3 \leq x \leq 3$, $x \in \mathbb{R}$ - Junior Cycle Mathematics - Question 10 - 2016
Step 1
Fill in the table below to show the value of $f(x)$ and the value of $f(x) - 2$ for each of the given values of $x$.
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Answer
To fill in the table for values of f(x) and f(x)−2, we reference the graph to find the corresponding f(x) values:
At x=−3, f(x)=2ightarrowf(x)−2=0
At x=−2, f(x)=4ightarrowf(x)−2=2
At x=−1, f(x)=4ightarrowf(x)−2=2
At x=0, f(x)=2ightarrowf(x)−2=0
At x=1, f(x)=0ightarrowf(x)−2=−2
At x=2, f(x)=−2ightarrowf(x)−2=−4
At x=3, f(x)=−4ightarrowf(x)−2=−6
Step 2
Hence, or otherwise, draw the graph of $y = f(x) - 2$ on the co-ordinate diagram above,
for $-3 \leq x \leq 3$, $x \in \mathbb{R}$.
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Answer
This graph can be drawn by taking the values from the previous table and plotting them.
The line segment will move downwards by 2 units for each corresponding x value of f(x).
The graph will pass through points:
(-3, 0)
(-2, 2)
(-1, 2)
(0, 0)
(1, -2)
(2, -4)
(3, -6)
Step 3
Fill in the table below to show the value of $h(x)$ for each of the given values of $x$.
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Answer
Using the graph for h(x), we find the values:
At x=−3, h(x)=2
At x=−2, h(x)=1
At x=−1, h(x)=0
At x=0, h(x)=−1
At x=1, h(x)=−1
At x=2, h(x)=0
At x=3, h(x)=1
Step 4
Hence, or otherwise, draw the graph of $y = [h(x)]^2$ on the co-ordinate diagram above,
for $-3 \leq x \leq 3$, $x \in \mathbb{R}$.
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Answer
The graph of y=[h(x)]2 can be derived from the values of h(x):
The values of h(x) from the table are squared.
Therefore, the resulting y values will be:
At x=−3, y=4
At x=−2, y=1
At x=−1, y=0
At x=0, y=1
At x=1, y=1
At x=2, y=0
At x=3, y=1
Plot these points and connect them to reveal the graph of y=[h(x)]2.
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