The co-ordinate diagram below shows the graph of the function $y = f(x)$ - Junior Cycle Mathematics - Question 12 - 2017
Question 12
The co-ordinate diagram below shows the graph of the function $y = f(x)$.
On the same axes, draw the graph of the line $g(x) = x + 3$, for $-3 \leq x \leq 5$, $x ... show full transcript
Worked Solution & Example Answer:The co-ordinate diagram below shows the graph of the function $y = f(x)$ - Junior Cycle Mathematics - Question 12 - 2017
Step 1
On the same axes, draw the graph of the line $g(x) = x + 3$, for $-3 \leq x \leq 5$
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Answer
To draw the line g(x)=x+3, start at the point (−3,0) since when x=−3, g(−3)=−3+3=0. This gives the coordinates (-3, 0). When x=5, the coordinates will be (5, 8). Connect the points with a straight line to depict the graph of g(x) on the same axes as f(x).
Step 2
Use the graphs to write down the points of intersection of $f(x)$ and $g(x)$
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Answer
The points of intersection can be determined by visually inspecting where the graphs of f(x) and g(x) meet. These points are approximately at (−1,2) and (2,5).
Step 3
Work out the value of $k(3)$
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Answer
To evaluate k(3), substitute 3 into the function:
k(3)=(3)2−2(3)−1=9−6−1=2
Thus, k(3)=2.
Step 4
Draw the graph of the function $k(x) = x^2 - 2x - 1$ on the axes below, for $-2 \leq x \leq 4$
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Answer
To sketch the graph of k(x)=x2−2x−1, first identify key points by calculating k(−2), k(0), k(2), and k(4):
k(−2)=1
k(0)=−1
k(2)=−1
k(4)=1
Plot these points and sketch a smooth curve to represent the parabolic shape of the function between the specified boundaries.
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