Question

Your friend hands you a graph of the performance statistics of the newest car to roll off the assembly line. He says, “I know this graph is f(x) = –4(x – 5)3 + 7 but I can’t remember how it is related to the graph of x3.” Explain to your friend how the graph f(x) is a translation of the graph x3

Answer 1

f(x) = –4(x – 5)^3 + 7
Start with x^3
First replace x by (x-5) to get (x-5)^3. This is equivalent to shifting the graph x^3 to the RIGHT by 5 units.
Then multiply by -4 so it becomes -4(x-5)^3. When multiplying by a negative number it is equivalent to turning the graph upside down or more precisely reflecting about the x-axis. And the number 4 will stretch the graph vertically by a factor of 4.
Add 7 so that it becomes -4(x-5)^3 + 7. This is equivalent to shifting the graph UP by 7 units.

Answer 2

Thnk u gut

Answer 3

guy