Question

h(x) = x² + 2x + 3

1. h(-3) to h(0)

f(x) = -x² + x - 3

1. f(3) to f(7)

1. y = 3x - 2

3,1

1. y = 4x - 12

5,4

Explanation:

Step1: Calculate h(-3)

Substitute $x=-3$ into $h(x)$:
$h(-3) = (-3)^2 + 2(-3) + 3 = 9 - 6 + 3 = 6$

Step2: Calculate h(-2)

Substitute $x=-2$ into $h(x)$:
$h(-2) = (-2)^2 + 2(-2) + 3 = 4 - 4 + 3 = 3$

Step3: Calculate h(-1)

Substitute $x=-1$ into $h(x)$:
$h(-1) = (-1)^2 + 2(-1) + 3 = 1 - 2 + 3 = 2$

Step4: Calculate h(0)

Substitute $x=0$ into $h(x)$:
$h(0) = 0^2 + 2(0) + 3 = 3$
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Step5: Calculate y at [3,1]

For $y=3x-2$, substitute $x=3$ then $x=1$:
$y(3)=3(3)-2=7$, $y(1)=3(1)-2=1$
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Step6: Calculate f(3)

Substitute $x=3$ into $f(x)$:
$f(3) = -(3)^2 + 3 - 3 = -9 + 3 - 3 = -9$

Step7: Calculate f(4)

Substitute $x=4$ into $f(x)$:
$f(4) = -(4)^2 + 4 - 3 = -16 + 4 - 3 = -15$

Step8: Calculate f(5)

Substitute $x=5$ into $f(x)$:
$f(5) = -(5)^2 + 5 - 3 = -25 + 5 - 3 = -23$

Step9: Calculate f(6)

Substitute $x=6$ into $f(x)$:
$f(6) = -(6)^2 + 6 - 3 = -36 + 6 - 3 = -33$

Step10: Calculate f(7)

Substitute $x=7$ into $f(x)$:
$f(7) = -(7)^2 + 7 - 3 = -49 + 7 - 3 = -45$
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Step11: Calculate y at [5,4]

For $y=4x-12$, substitute $x=5$ then $x=4$:
$y(5)=4(5)-12=8$, $y(4)=4(4)-12=4$

Answer:

1. $h(-3)=6$, $h(-2)=3$, $h(-1)=2$, $h(0)=3$
2. At $x=3$, $y=7$; at $x=1$, $y=1$
3. $f(3)=-9$, $f(4)=-15$, $f(5)=-23$, $f(6)=-33$, $f(7)=-45$
4. At $x=5$, $y=8$; at $x=4$, $y=4$