Question

6 Andre graphed the parent function f(x) anda new line d(x). If d(x) will have a slope ofand a y-intercept of 9, write a function torepresent d(x) as a transformation of f(x).

Answer 1

You have the parent function f(x) given by:

$f(x)=x$

(this function is the simplest form of a line in the coordinate plane).

To obtain a line d(x) with a slope of 1/4 and a y-intercept of 9, first, it is necessary to multiply the parent function by 1/4 (this is the first transformation):

$T_1\lbrack f(x)\rbrack\Rightarrow\frac{1}{4}f(x)=\frac{1}{4}x$

next, add 9 to the previous result (this is the second transformation):

$T_2\lbrack\frac{1}{4}f(x)\rbrack=\frac{1}{4}f(x)+9=\frac{1}{4}x+9$

Thus, to obtain the required linear function d(x), the previous T1 and T2 transformations are needed. The last result is a line with slope 1/4 and y-intercept 9.