Question

A certain function is defined as “multiply the input by negative one half, then add 3.”

Which graph represents this function?
Responses
A Image with alt text:
B Image with alt text:
C Image with alt text:
D Image with alt text:

Answer 1

To represent the function defined as “multiply the input by negative one half, then add 3,” we can express the function mathematically. If we let \( x \) be the input, the function can be written as:

\[ f(x) = -\frac{1}{2}x + 3 \]

This equation represents a linear function in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In our case:

- The slope \( m = -\frac{1}{2} \) indicates that the line will fall as you move from left to right (since the slope is negative).
- The y-intercept \( b = 3 \) tells us that the line crosses the y-axis at the point (0, 3).

To find the graph that represents this function, look for a line that:

1. Has a y-intercept at (0, 3).
2. Slopes downward as you move from left to right, meaning for every 2 units you move to the right, you would move 1 unit down.

If you can provide me with the images or more descriptions of the graphs, I can help you determine which one matches the function.