Questions: Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function.

Transcript text: Consider the following graph of $g(x)$. Write a formula for $g(x)$ that describes the transformations performed on the basic function.

Solution

Solution Steps

Step 1: Identify the basic function

The graph resembles a cubic function, _f(x) = x³_.

Step 2: Determine the horizontal shift

The inflection point of the basic cubic function is at (0,0). This graph's inflection point is at (-5, 2). This indicates a horizontal shift 5 units to the left.

Step 3: Determine the vertical shift

The horizontal shift moves the inflection point from (0, 0) to (-5, 0). Because the inflection point of the provided graph is at (-5, 2), there's a vertical shift upwards of 2 units.

Final Answer: The formula for g(x) is g(x) = (x+5)³ + 2.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!