Question

Select the correct statement about f(x) = 5x − 9. Responses Translating f(x) horizontally by 5 changes the y-intercept to 16. Translating f(x) horizontally by 5 changes the y-intercept to 16. Translating f(x) vertically by −3 does not change the y-intercept. Translating f(x) vertically by −3 does not change the y-intercept. Horizontally stretching f(x) by 3 changes the slope to 8. Horizontally stretching f(x) by 3 changes the slope to 8. Vertically stretching f(x) by 2 changes the slope to 10.

Answer 1

Vertically translating the function f(x) = 5x − 9 by −3 does not change the y-intercept. The other options given, such as horizontal translation or stretching, are incorrectly described in the context of the function's slope and y-intercept.

Step-by-step explanation:

The correct statement about the function f(x) = 5x − 9 is that translating f(x) vertically by −3 does not change the y-intercept. When you translate a function vertically, you are adding or subtracting a constant to the entire function, which shifts the graph up or down without affecting the x-coordinates of the points on the graph, including the y-intercept. Now, addressing the other statements, translating the function horizontally will not affect the y-intercept; it will only shift the graph left or right. Stretching a function horizontally by a factor will change the slope of the function, but in this case, it would be the reciprocal of 3 (not 8), because you stretch by taking the original slope and dividing by the stretching factor. Finally, stretching the function vertically by a factor (like 2) will multiply the slope by that factor; however, the function f(x) already has a slope of 5, not 3 as indicated in Figure A1, thus vertically stretching it by 2 would result in a new slope of 10.