Question

The graph of F(x) shown below resembles the graph of G(x)= x4, but it has
been vertically stretched. Which of the following could be the equation of F(X)
?

Answer 1

Answer:

• x = 0.

Equation:

• $g*(x)-(x^4)=0$

Step-by-step explanation:

Step 1:

• Pull out like factors:
• $gx - x^4 = x * (g - x^3)$

Trying to factor as a Difference of Cubes:

• Factoring: $g - x^3$
• Theory : A difference of two perfect cubes,  a^3 - b^3 can be factored into
•              (a-b) • (a^2 +ab +b^2)
• Proof :  (a-b)•(a^2+ab+b^2) =
•            a^3+a^2b+ab^2-ba^2-b^2a-b^3 =
•            a^3+(a^2b-ba^2)+(ab^2-b^2a)-b^3 =
•            a^3+0+0-b^3 =
•            a^3-b^3
• Check :  g^1 is not a cube !!
• Ruling : Binomial cannot be factored as the difference of two perfect cubes

Equation at end of step 1:

• $x * (g - x^3) = 0$

Step 2:

•  A product of several terms equals zero.
• When a product of two or more terms equals zero, then at least one of the terms must be zero.
• We shall now solve each term = 0 separately
• In other words, we are going to solve as many equations as there are terms in the product
• Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

• Solve $g - x^3 = 0$
• In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
• We shall not handle this type of equations at this time.

Solution:

• x=0.