2.2 Linear transformation practice 1

Describe linear transformations from the parent function [math]f(x)=|x|[/math] to [math]g(x)=2|-x-2|-2[/math].

Describe linear transformations from the parent function [math]f(x)=x^3[/math] to [math]g(x)=-(4(x-3))^3+2[/math].

Let [math]f(x)[/math] be a function. Which of the following function(s) having the same [math]x[/math]-intercepts as [math]f(x)[/math]?

Let [math]f(t)=1000-997\cdot(0.8)^t[/math] be a function representing the height of the airplane where [math]t[/math] is measured in seconds and [math]f(t)[/math] is measured in meters. Suppose we want to change the unit of height from meters to kilometers and the unit of time from seconds to hours. What is the new function?

Let [math]f(x)=\dfrac{1}{x^2+1}[/math]. We stretch [math]f(x)[/math] by the factor 2 horizontally and vertically, and translate 4 units left and 1 unit up. What is the new function?

Let [math]f(x)=2x^3-6[/math]. We reflect [math]f(x)[/math] about the [math]y[/math]-axis, compress by the factor 3 vertically, and translate 4 units to the left. What is the new function?

The graph of function [math]f(x)=\sqrt{1^2-x^2}[/math] is an upper semicircle with center [math](0,0)[/math] and radius 1. If the graph of [math]g(x)=3f\left(\dfrac{1}{3}x\right)-3[/math] is also an upper semicircle, what is the center and radius of [math]g(x)[/math]?

Consider a linear function [math]f(x)=-\dfrac{1}{4}x-3[/math] where [math]m[/math] is negative. If the graph of [math]g(x)=f(x-k)[/math] does not pass the third quadrant where [math]k[/math] is an integer, what is the minimum of [math]k[/math]?

The table shows some values of function [math]f(x)[/math]. If [math]g(x)=-f(x-2)+4[/math], which of the following values is largest?

Let [math]f(x)[/math] be a function having two [math]x[/math]-intercepts [math]3[/math] and [math]-2[/math]. If [math]g(x)=-2f\left(\dfrac{1}{3}x+3\right)[/math]. What is the summation of the [math]x[/math]-intercepts of [math]g(x)[/math]?