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An exponential function with a base of 1/2 has been compressed vertically by a factor of 3/4 and reflected in the y-axis. Its asymptote is the line y = -4. Its y-intercept is (0,-13/4).

a) Write an equation of the function.

b) Discuss its domain and range

Jul 15, 2021

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a) Write an equation of the function.

b) Discuss its domain and range

Hello Guest!

a)

$$f(x)=\frac{3}{4}\cdot (\frac{1}{2})^x-4\\ f(0)=-\frac{13}{4}$$

reflected

$$g(x)=\frac{3}{4}\cdot (\frac{1}{2})^{-x}-4\\ g(0)=-\frac{13}{4}$$

b)

domain f(x) and g(x) : $$-\infty$$ < x < $$\infty$$

range f(x) : - 4 < f(x) < $$\infty$$

range g(x) : - 4 < g(x) < $$\infty$$

!

Jul 16, 2021
edited by asinus  Jul 16, 2021