Questions: Score: 0/18 Answered: 0/18 Question 1 If the formula (y=x^3) is changed by adding four (shown in bold below), what effect would that change have on the function's values? (f(x)=x^3+4)

Score: 0/18 Answered: 0/18
Question 1

If the formula (y=x^3) is changed by adding four (shown in bold below), what effect would that change have on the function's values?

(f(x)=x^3+4)

Transcript text: Score: 0/18 Answered: 0/18 Question 1 If the formula $y=x^{3}$ is changed by adding four (shown in bold below), what effect would that change have on the function's values? \[ f(x)=x^{3}+4 \] Select an answer What effect would it have on the graph? Select an answer

Solution

Solution Steps

Step 1: Analyze the Effect on Function Values

The original function is $ y = x^{3} $. When 4 is added to the function, it becomes $ f(x) = x^{3} + 4 $. This means that for every input $ x $, the output $ y $ is increased by 4 compared to the original function.

Step 2: Determine the Effect on the Graph

Adding 4 to the function $ y = x^{3} $ results in a vertical shift of the graph. Specifically, the graph of $ f(x) = x^{3} + 4 $ is the graph of $ y = x^{3} $ shifted upward by 4 units.

Step 3: Conclusion

The change $ f(x) = x^{3} + 4 $ increases all function values by 4 and shifts the graph of the function upward by 4 units.