Answer:
1) shifts f(x) 4 units down = g(x) = [tex]2x-10[/tex]
2) stretches by factor 4 = g(x) = [tex]8x-24[/tex]
3) shifts f(x) 4 units right = g(x) = [tex]2x-14[/tex]
4) compresses by factor 4 = g(x) = [tex]8x-6[/tex]
Step-by-step explanation:
1) When we have to move the function down by 4 units, subtract the whole function by -4, that is y -4.
Thus, f(x) becomes g(x) = [tex]2x-6-(4)[/tex] = [tex]2x-10[/tex]
2) When the function is stretched away from x axis, it means in Y direction.
Thus, when stretched 4 units in Y direction, the function becomes 4(f(x))
= g(x) = [tex]4(2x-6)[/tex] = [tex]8x-24[/tex]
3)When we have to move the function right by 4 units, replace x with (x-4) in the function.
Thus, f(x) becomes g(x) = [tex]2(x-4)-6[/tex] = [tex]2x-8-6[/tex] = [tex]2x-14[/tex]
4) When the function is stretched towards y axis, it means in X direction.
Thus, when compressed 4 units in X direction, replace the x by 4x.
= g(x) = [tex]2(4x)-6[/tex] = [tex]8x-6[/tex]
