Parent Functions Quick Check. Use Equation A and describe the differences to show t...
Check the final answer first, then review the worked steps.
Problem
Parent Functions Quick Check. Use Equation A and describe the differences to show the change from f(x) = x to the equation A. Equation A: f(x) = 3x - 4.
Answer
The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units.
Step-by-step solution
- Identify the parent function: The problem states the change is from $f(x) = x$. This is the identity parent function, which has a slope of 1 and a y-intercept of 0.
- Identify Equation A: Equation A is given as $f(x) = 3x - 4$.
- Compare the slopes: The slope of the parent function $f(x) = x$ is 1. The slope of Equation A, $f(x) = 3x - 4$, is 3. To get from a slope of 1 to a slope of 3, the slope increases by a factor of 3 (since $1 \times 3 = 3$).
- Compare the y-intercepts: The y-intercept of the parent function $f(x) = x$ is 0 (since it can be written as $f(x) = 1x + 0$). The y-intercept of Equation A, $f(x) = 3x - 4$, is -4. A change in the y-intercept from 0 to -4 means the graph moves down the y-axis by 4 units.
- Combine the changes: The slope increases by a factor of 3, and the graph moves down the y-axis by 4 units.