Find the x and y Intercepts f(x)=(4/3)^x

Problem

ƒ(x)=(4/3)^x

Solution

1. Find the y-intercept by setting x=0 and evaluating the function.

ƒ(0)=(4/3)^0

2. Simplify the expression using the zero exponent rule, which states that any non-zero base raised to the power of zero is 1

ƒ(0)=1

3. Identify the y-intercept as the point where the graph crosses the y-axis.

(0,1)

4. Find the x-intercept by setting ƒ(x)=0 and solving for x

0=(4/3)^x

5. Analyze the equation for the x-intercept. Since an exponential function with a positive base b^x is always greater than zero for all real x there is no value of x that satisfies the equation.

(4/3)^x>0

6. Conclude that there are no x-intercepts for this function.

No x-intercept

Final Answer

x-intercept: none, y-intercept: *(0,1)

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