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 (1 point) Responses The slope decreases by a factor of 3 and the graph of the function moves up the y-axis 4 units. The slope decreases by a factor of 3 and the graph of the function moves up the y -axis 4 units. The slope decreases by a factor of 3 and the graph of the function moves down the y-axis 4 units. The slope decreases by a factor of 3 and the graph of the function moves down the y -axis 4 units. The slope increases by a factor of 3 and the graph of the function moves up the y-axis 4 units. The slope increases by a factor of 3 and the graph of the function moves up the y -axis 4 units. The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units. The slope increases by a factor of 3 and the graph of the function moves down the y -axis 4 units.

Question

GPT-4o mini · Answer

To compare the functions $ f(x) = x $ and $ f(x) = 3x - 4 $, we can analyze the slope and the y-intercept of both equations. 1. **Slope**: - The slope of $ f(x) = x $ is 1 (since it can be expressed as $ f(x) = 1x + 0 $). - The slope of $ f(x) = 3x - 4 $ is 3. - Thus, we see the slope **increases** from 1 to 3, not decreases. 2. **Y-Intercept**: - The y-intercept of $ f(x) = x $ is 0 (the value of $ f(0) $). - The y-intercept of $ f(x) = 3x - 4 $ is -4 (the value of $ f(0) $). - Therefore, the graph of the function moves **down** the y-axis 4 units. Based on this analysis, the correct interpretation is: "The slope increases by a factor of 3 and the graph of the function moves down the y-axis 4 units." None of the original given options perfectly match this assessment, as they mention a decrease in slope instead of an increase. The correct explanation should be that the slope increases, and the graph moves down 4 units.