https://file.aiquickdraw.com/mathbot/file/17272915959120ks026ph.jpg

The graph shows a straight line with a slope of 1 (it increases by 1 unit up for every 1 unit to the right). The parent function for this graph appears to be \( f(x) = x \), which is a basic linear function with a slope of 1 and a y-intercept at the origin (0, 0).

Now, examining the graph in your image, the line has been shifted, but the slope remains the same. The key difference is the y-intercept, which appears to be at \( y = 3 \). This indicates a vertical shift of the graph of \( f(x) \).

The correct transformation would be a vertical translation *up* by 3 units. Thus, the answer is:

**C. The graph of the function is translated up 3 units.**

Would you like further details or have any other questions?

Here are 5 related questions:
1. How does a vertical shift affect the equation of a function?
2. What is the general form of a linear function after translation?
3. What happens if a graph is translated both horizontally and vertically?
4. How does the slope of a line help in identifying transformations?
5. How would a reflection over the x-axis change this graph?

**Tip:** For linear functions, translations change only the intercepts, not the slope!

What is the effect on the graph of the parent function f(x)?

Discover how the graph of the parent function f(x) = x is translated vertically. In this problem, the graph undergoes a vertical shift up by 3 units. Explore key concepts like linear functions, slope-intercept form, and graph transformations. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation