The functions and their matching properties are:
- [tex]h(x) = f(x - \frac{1}{2}) \to[/tex] x-intercept at (1.5,0)
- [tex]j(x) = f(x) - \frac{1}{2} \to[/tex] vertical asymptote x = 0
- [tex]g(x) = -\frac 12f(x - 2) \to[/tex] function decreases as x increases
How to match the functions with their properties?
To do this, we start by plotting the graphs of the functions h(x), j(x) and g(x)
Next, we list out the properties from the graphs
From the graphs of the functions (see attachment), we have the following highlights:
- [tex]h(x) = f(x - \frac{1}{2})[/tex] has an x-intercept of (1.5,0)
- [tex]j(x) = f(x) - \frac{1}{2}[/tex] has a vertical asymptote of x = 0
- The function [tex]g(x) = -\frac 12f(x - 2)[/tex] decreases as x increases
Read more about functions at:
https://brainly.com/question/1851758
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