Answer:
- f(x): vertical, x = -4; horizontal, y = 3
- g(x): vertical, x = 2; horizontal, y = -4
- g(x) is shifted right 6 and down 7 from f(x)
Step-by-step explanation:
The vertical asymptote is the vertical dashed line in each graph. Its equation is x = constant, where the constant can be read from the graph where the line crosses the x-axis.
The horizontal asymptote is the horizontal dashed line in each graph. Its equation is y = constant, where the constant can be read from the graph where the line crosses the y-axis.
f(x)
The vertical asymptote is x = -4. The horizontal asymptote is y = 3.
g(x)
The vertical asymptote is x = 2. The horizontal asymptote is y = -4.
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The vertical asymptote of g(x) is 2-(-4) = 6 units to the right of that of f(x). The horizontal asymptote of g(x) is -4-3 = -7 units up from that of f(x). The graph of g(x) matches that of f(x) shifted right 6 units and down 7 units.
