Complete the table below to show the value of the function $f(x) = -x^2 - x + 6$ for each of the given values of $x$ - Leaving Cert Mathematics - Question b - 2020
Question b
Complete the table below to show the value of the function $f(x) = -x^2 - x + 6$ for each of the given values of $x$.
| x | -4 | -3 | -2 | -1 | 0 | 2 |
|----|----|... show full transcript
Worked Solution & Example Answer:Complete the table below to show the value of the function $f(x) = -x^2 - x + 6$ for each of the given values of $x$ - Leaving Cert Mathematics - Question b - 2020
Step 1
Complete the table for $f(x)$
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Answer
To complete the table, we substitute the given values of x into the function f(x)=−x2−x+6:
For x=−4:
f(−4)=−(−4)2−(−4)+6=−16+4+6=−6
For x=−3:
f(−3)=−(−3)2−(−3)+6=−9+3+6=0
For x=−2:
f(−2)=−(−2)2−(−2)+6=−4+2+6=4
For x=−1:
f(−1)=−(−1)2−(−1)+6=−1+1+6=6
For x=0:
f(0)=−(0)2−(0)+6=6
For x=2:
f(2)=−(2)2−(2)+6=−4−2+6=0
Thus, the completed table is:
x
-4
-3
-2
-1
0
2
f(x)
-6
0
4
6
6
0
Step 2
Draw the graph of $f$ in the domain $-4 \leq x \leq 2$
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Answer
To graph the function f(x)=−x2−x+6, plot the points from the completed table:
The points to plot are:
(−4,−6)
(−3,0)
(−2,4)
(−1,6)
(0,6)
(2,0)
Connect these points smoothly to depict the graph of f(x) in the specified domain.
Step 3
Draw the graph of $g(x) = f(x - 2)$
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Answer
To graph the function g(x)=f(x−2), we need to determine how the graph of f(x) shifts. Since g(x) represents a horizontal shift to the right by 2 units:
The domain for g(x) is −2≤x≤4.
We take the points from the graph of f and shift them:
(−4,−6)→(−2,−6)
(−3,0)→(−1,0)
(−2,4)→(0,4)
(−1,6)→(1,6)
(0,6)→(2,6)
(2,0)→(4,0)
Plot these points for g(x) on the same graph as f(x) and connect them smoothly, ensuring to label the graphs of f(x) and g(x) clearly.
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