Functions can be transformed from one to another through transformations such as dilation, reflection. rotation and translation. See attachment for the graph of [tex]y =\frac{1}{2}f(x)[/tex]
Given that:
[tex]f(x) = -\frac 12x - 3[/tex]
[tex]y = f(x)[/tex] means that:
[tex]y = -\frac 12x - 3[/tex]
When the graph is transformed to [tex]y =\frac{1}{2}f(x)[/tex]
The equation becomes:
[tex]y = \frac 12 \times (-\frac 12x - 3)[/tex]
Open bracket
[tex]y = -\frac 14x - \frac 32[/tex]
To graph [tex]y =\frac{1}{2}f(x)[/tex], we simply calculate the intercepts.
Calculate y-intercept i.e. [tex]x =0[/tex]
[tex]y = -\frac 14x - \frac 32[/tex]
[tex]y = -\frac 14 \times 0 - \frac 32[/tex]
[tex]y = - \frac 32[/tex]
[tex]y = -1.5[/tex]
So, the first coordinate is represented as:
[tex](x_1,y_1) = (0,-1.5)[/tex]
Calculate x-intercept i.e. [tex]y = 0[/tex]
[tex]0 = -\frac 14x - \frac 32[/tex]
Collect like terms
[tex]\frac 14x = - \frac 32[/tex]
Multiply through by 4
[tex]4 \times \frac 14x = - \frac 32 \times 4[/tex]
[tex]x = -3 \times 2[/tex]
[tex]x = -6[/tex]
The next coordinate is represented as:
[tex](x_2,y_1) = (-6,0)[/tex]
This means that the graph of [tex]y =\frac{1}{2}f(x)[/tex] is a straight line that passes through (0,-1.5) and (-6,0)
See attachment for the graph of [tex]y =\frac{1}{2}f(x)[/tex]
Read more about function and graphs at:
https://brainly.com/question/18806107
