Find the values for c and d that would make the following equation true. (-9y^c)(dy^7)=36y^9
1 answer:
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-5 = 
- 2 equals x = -4.
First, simplify to 
. / Your problem should look like: -5 = - 2.
Second, multiply both sides by 4. / Your problem should look like: -20 = 3x -8.
Third, add 8 to both sides. / Your problem should look like: -20 + 8 = 3x.
Fourth, simplify -20 + 8 to -12. / Your problem should look like: -12 = 3x.
Fifth, divide both sides by 3. / Your problem should look like:
= x.
Sixth, simplify
to 4. / Your problem should look like: -4 = x.
Seventh, switch sides. / Your problem should look like: x = -4, which is your answer.
First, simplify
Second, multiply both sides by 4. / Your problem should look like: -20 = 3x -8.
Third, add 8 to both sides. / Your problem should look like: -20 + 8 = 3x.
Fourth, simplify -20 + 8 to -12. / Your problem should look like: -12 = 3x.
Fifth, divide both sides by 3. / Your problem should look like:
Sixth, simplify
Seventh, switch sides. / Your problem should look like: x = -4, which is your answer.
Let's analyze the changes made to the parent function one by one:
STEP 1: Horizontal translation.
If we transform
We're performing a change in the form of
This kind of changes result in a horizontal translation, k units to the left if k is positive, k units to the right if k is negative. In this case, k=2, so the original graph is shifted 2 units to the left.
STEP 3: Vertical stretch.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical stretch with scale factor k. If k is negative, the function is also reflected across the x axis. In this case, k=3, so the original graph is stretched vertically, with scale factor 3.
STEP 3: Vertical translation.
If we transform
We're performing a change in the form of
This kind of changes result in a vertical translation, k units down if k is positive, k units up if k is negative. In this case, k= -4, so the graph is shifted 4 units down.
All, in all, the original graph is shifted 2 units to the right, then it's stretched vertically with scale 3, and then it's shifted 4 units down. The order is important!