Question

Use equation a and describe the difference to show the change from f of x equals x to the equation a f of x equals 3x - 4
The slope increases by a factor of 3 and the graph of the function moves up the y-axis four units the slope decreases by the factor of 3 in the graph of the function moves down the y-axis four units the slope increases by a factor of 3 and the graph of the function moves down the y-axis for units the slope decreases by a factor of 3 and the graph of the function moves up the y-axis four units

Answer 1

To analyze the transformation from the function \( f(x) = x \) to the new function \( a f(x) = 3x - 4 \), let's break it down using the following steps:

1. **Original Function**:
- The function \( f(x) = x \) has a slope (or coefficient of \( x \)) of 1.

2. **New Function**:
- The function \( a f(x) = 3x - 4 \) has a slope of 3 (the coefficient of \( x \)) and a y-intercept of \(-4\).

### Changes Observed:

- **Slope Change**:
- The slope of the new function \( 3x - 4 \) is 3, which is an increase from the original slope of 1 (i.e., the slope increased by a factor of \( \frac{3}{1} = 3 \)).

- **Vertical Shift**:
- The new function has a y-intercept of \(-4\), which means the graph of the function moves **downwards** on the y-axis by 4 units (since the original function crossed the y-axis at \( y = 0 \) and the new function crosses at \( y = -4 \)).

### Conclusion:
Therefore, the best description of the transformation is:

**The slope increases by a factor of 3, and the graph of the function moves down the y-axis 4 units.**