Complete the following table for the function $f: x \mapsto -x^2 - 3x - 2$ in the domain $-2 \leq x \leq 4$ - Junior Cycle Mathematics - Question 14 - 2013
Question 14
Complete the following table for the function $f: x \mapsto -x^2 - 3x - 2$ in the domain $-2 \leq x \leq 4$.
| x | f(x) | (x, f(x)) |
|----|------|-----------|
| -... show full transcript
Worked Solution & Example Answer:Complete the following table for the function $f: x \mapsto -x^2 - 3x - 2$ in the domain $-2 \leq x \leq 4$ - Junior Cycle Mathematics - Question 14 - 2013
Step 1
Complete the table for the function
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Answer
To complete the table, we need to calculate the values of f(x) for each x. The function is given by:
f(x)=−x2−3x−2
Now, let's find the values:
For x=−2:
f(−2)=−(−2)2−3(−2)−2=−4+6−2=8
For x=−1:
f(−1)=−(−1)2−3(−1)−2=−1+3−2=0
For x=0:
f(0)=−(0)2−3(0)−2=−2
For x=1:
f(1)=−(1)2−3(1)−2=−1−3−2=−6
For x=2:
f(2)=−(2)2−3(2)−2=−4−6−2=−12
For x=3:
f(3)=−(3)2−3(3)−2=−9−9−2=−20
For x=4:
f(4)=−(4)2−3(4)−2=−16−12−2=−30
Thus, the completed table is:
x
f(x)
(x, f(x))
-2
8
(-2, 8)
-1
0
(-1, 0)
0
-2
(0, -2)
1
-6
(1, -6)
2
-12
(2, -12)
3
-20
(3, -20)
4
-30
(4, -30)
Step 2
Draw the graph of the function
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Answer
Using the values from the completed table, we plot the points on a Cartesian coordinate system. The points to plot are:
(-2, 8)
(-1, 0)
(0, -2)
(1, -6)
(2, -12)
(3, -20)
(4, -30)
After plotting these points, we can connect them to visualize the graph of the function. The resulting graph will be a downward-opening parabola as the leading coefficient of the x2 term is negative.
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