SOLUTION: State the intercepts and asymptotes for f and f-1 f(x)= (4^x-2)-3

Question 813636: State the intercepts and asymptotes for f and f-1
f(x)= (4^x-2)-3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First, please put parentheses around exponents, especially if they are more than just a positive integer or variable. What you posted meant:

but I think you meant:

Problems that are clearly posted are more likely to get a quick response.

To find the y-intercept of f(x), make the x equal to zero:

Y-intercept: (0, -47/16)

To find the x-intercept(s), make the y be zero:

X-intercept: (, 0)

Since f(x) is an exponential function and since exponents can be any number, there are no vertical asymptotes. There is a horizontal asymptote. As x approaches negative infinity the exponent of approaches negative infinity, too. And as the exponent approaches negative infinity value of approaches zero. And since approaches zero, f(x) approaches -3. So:
Horizontal asymptote: y = -3

Finding these for the inverse is easy since for the inverse, the x's and y's have traded places. So the inverse's intercepts will be the function's intercepts with the x's and y's trading places and the inverse's asymptote will be the function's asymptote with the x's and y's trading places:



function                        inverse

Y-intercept: (0, -47/16)        X-intercept: (-47/16, 0)

X-intercept: (, 0)     Y-intercept: (0, )

Horizontal asymptote: y = -3    Vertical asymptote: x = -3 

RELATED QUESTIONS

Thank you for your help!

Sketch each function. State the domain, range, values of... (answered by Fombitz)
f(x) 3(x-1) (x=4)state the x intercepts and the y... (answered by oberobic)
Sketch the graph of f(x)= (3(x^2^-4))/x^2^-1
Give the X and Y INTERCEPTS (as points) and  (answered by lwsshak3)
Sketch the graph of f(x)= (3(x^2-4))/x^2-1 give the x and y intercepts and the horizontal  (answered by lynnlo)
SKETCH THE GRAPH of f(x)= (3(x^2-4))/x^2-1 give the X and Y INTERCEPTS and the HORIZONTAL  (answered by stanbon)
4.	Sketch the graph of f(x) = 2x^2 / (x^2+2x -3) and give its domain, intercepts and... (answered by ewatrrr)
What is the domain, intercepts, and asymptotes of f(x)=ln(x^2 +... (answered by Fombitz)
Can you identify the intercepts and asymptotes of this equation?

f(x) = (3x) / (x^2 +... (answered by mducky2)
Find the x-intercepts and y intercepts for f(x) f(x)... (answered by oscargut)