# The point (-12, 4) is on the graph of y = f(x). Find the corresponding point on the graph of y = g(x)? (Refer to below)

## 1) $g \left(x\right) = \frac{1}{2} f \left(x\right)$ 2) $g \left(x\right) = f \left(x - 2\right)$ 3) $g \left(x\right) = f \left(- x\right)$ 4) $g \left(x\right) = f \left(4 x\right)$ 5) $g \left(x\right) = 4 f \left(x\right)$ 6) $g \left(x\right) = - f \left(x\right)$ I know the answers for 1, 3, and 5 are (-12, 2), (12, 4), and (-12, 16) respectively, but I don't know how to solve them.

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John D. Share
Oct 13, 2017

#### Answer:

1. $\left(- 12 , 2\right)$
2. $\left(- 10 , 4\right)$
3. $\left(12 , 4\right)$
4. $\left(- 3 , 4\right)$
5. $\left(- 12 , 16\right)$
6. $\left(- 12 , - 4\right)$

#### Explanation:

1:

Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value ($4$) and divide it by 2 to get $2$.

Therefore, the new point is $\left(- 12 , 2\right)$

2:

Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value ($- 12$) to get $- 10$.

Therefore, the new point is $\left(- 10 , 4\right)$

3:

Making the input of the function negative will multiply every x-value by $- 1$. To get the new point, we will take the x-value ($- 12$) and multiply it by $- 1$ to get $12$.

Therefore, the new point is $\left(12 , 4\right)$

4:

Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value ($- 12$) by $4$ to get $- 3$.

Therefore, the new point is $\left(- 3 , 4\right)$

5:

Multiplying the whole function by $4$ increases all y-values by a factor of $4$, so the new y-value will be $4$ times the original value ($4$), or $16$.

Therefore, the new point is $\left(- 12 , 16\right)$

6:

Multiplying the whole function by $- 1$ also multiplies every y-value by $- 1$, so the new y-value will be $- 1$ times the original value ($4$), or $- 4$.

Therefore, the new point is $\left(- 12 , - 4\right)$

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