2.2 Linear transformation practice 2

Let [math]f(x)[/math] be a nonlinear function passing through [math](0,-3)[/math] and [math](4,0)[/math]. If [math]g(x)=3f(-2x)[/math], what is the summation of the [math]x[/math]-intercept and [math]y[/math]-intercept of [math]g(x)[/math]?

Let [math]f(x)[/math] and [math]g(x)[/math] be two functions. If [math]f(2x+4)=-3g(x)-4[/math]. Describe the linear transformation from [math]f(x)[/math] to [math]g(x)[/math].

Let [math]f(x)[/math] be a function. If [math]f(2x)=2f(x)[/math], which of the following function(s) could be [math]f(x)[/math]?

The domain of function [math]f[/math] is all numbers between [math]-4[/math] and [math]6[/math] inclusive, and the range is all numbers between [math]-3[/math] and [math]5[/math], inclusive. What are the domain and range of [math]g(x)=3f(\dfrac{x}{2})[/math]?

The domain of [math]f(x)[/math] is [math][-4,6][/math], and the range is [math][-3,5][/math]. Given [math]g(x)=3f(x+1)+5[/math], what are the domain and range of [math]g(x)[/math]?

If [math]f(x)=x^2-2x+3[/math], which of the following is equal to [math]g(x)=f(x+1)[/math]?

The figure below is [math]f(x)[/math], which of the following is the graph of [math]y=k-f(x)[/math], where [math]k[/math] is a positive number?

The graphs of the functions [math]f[/math] and [math]g[/math] are shown above. Which of the following true?

In the figure above, a portion of the graph of [math]y=f(x)[/math] is shown. What are the coordinates of the [math]y[/math]-intercept of the graph of [math]y=f(x+2)[/math]?

(Calculator) If [math]f(x)=x^4-4x+1[/math] and [math]g(x)=f(x+2)[/math], which of the following statements are true?
I. [math]f[/math] and [math]g[/math] have one common zero.
II. The graphs of [math]f[/math] and [math]g[/math] have one intersection point.
III. [math]f[/math] and [math]g[/math] have the same range.