the graph of function g is a vertical translation of the graph of polynomial f. 4. the function h can be…
the graph of function g is a vertical translation of the graph of polynomial f. 4. the function h can be written in terms of f as h(x)=f(x)-2.5. complete the h(x) column of the table. 5. sketch the graph of function h. x f(x) h(x)=f(x)-2.5 -4 0 -3 -5.8 -0.7 0 1.2 -3.3 2 0
Answer
Explanation:
Step1: Recall the transformation rule
Given $h(x)=f(x)-2.5$, we subtract 2.5 from each $f(x)$ - value to get $h(x)$ - values.
Step2: Calculate $h(x)$ for $x = - 4$
Since $f(-4)=0$, then $h(-4)=f(-4)-2.5=0 - 2.5=-2.5$.
Step3: Calculate $h(x)$ for $x=-3$
Since $f(-3)=-5.8$, then $h(-3)=f(-3)-2.5=-5.8 - 2.5=-8.3$.
Step4: Calculate $h(x)$ for $x=-0.7$
Since $f(-0.7)=0$, then $h(-0.7)=f(-0.7)-2.5=0 - 2.5=-2.5$.
Step5: Calculate $h(x)$ for $x = 1.2$
Since $f(1.2)=-3.3$, then $h(1.2)=f(1.2)-2.5=-3.3 - 2.5=-5.8$.
Step6: Calculate $h(x)$ for $x = 2$
Since $f(2)=0$, then $h(2)=f(2)-2.5=0 - 2.5=-2.5$.
Answer:
| x | f(x) | h(x)=f(x)-2.5 |
|---|---|---|
| -4 | 0 | -2.5 |
| -3 | -5.8 | -8.3 |
| -0.7 | 0 | -2.5 |
| 1.2 | -3.3 | -5.8 |
| 2 | 0 | -2.5 |