Question

What is the equation of the graph that represents the parent function f(x)= x^4 stretched vertically by a factor of 2, then shifted down 3 spaces

Answer 1

To find the equation of a graph representing a stretched and shifted function, multiply the original function by the stretch factor and subtract the shift amount.

Step-by-step explanation:

The equation of the graph that represents the parent function f(x) = x^4 stretched vertically by a factor of 2 and shifted down 3 units can be determined as follows:

1. Start with the parent function f(x) = x^4.
2. To stretch the function vertically by a factor of 2, multiply the whole function by 2, resulting in 2x^4.
3. To shift the function down 3 units, subtract 3 from the whole function, resulting in 2x^4 - 3.

Therefore, the equation of the graph is y = 2x^4 - 3.