Question

If the formula y=x³ is changed by adding four as shown in red below, f(x)=(x+4)³.

a) Which values would be most directly affected by the change? Would it affect the x or y axis?
b) What effect would it have on the graph?
a- It would shift all the points to the right by four.
b- It would shift all the points down by four.
c- It would shift all points up by four.
d- It would have no effect.
e- It would shift all points to the left by four.

Answer 1

Modifying the function from f(x)=x³ to f(x)=(x+4)³ will result in the graph shifting all points to the left by four units on the x-axis, which directly affects the x-values of the function.

Step-by-step explanation:

When the function f(x) = x³ is modified to f(x) = (x+4)³, the values of x will be most directly affected, meaning that the graph will shift along the x-axis. This typically results in a translation or shift of the graph. For the function in question, every x-value of the function is being increased by 4 before being cubed, therefore the entire graph shifts to the left by 4 units. So the graph will shift by moving every point 4 units to the left on the x-axis.

Looking at the multiple-choice options provided:

• a) It would shift all the points to the right by four. (Incorrect)
• b) It would shift all the points down by four. (Incorrect)
• c) It would shift all points up by four. (Incorrect)
• d) It would have no effect. (Incorrect)
• e) It would shift all points to the left by four. (Correct)