Question

Use the drawing tools to form the correct answers on the graph Consider function f(x)= ( 1 2 )^ x ,x<=0\\ 2^ x ,&x>0 Complete the table of values for function and then plot the ordered pairs on the graph. - 2 -1 1 2 f(x)

Answer 1

$\begin{gathered} \text{for }f\mleft(x\mright)=1/2^x\colon\text{ 4, 2, 1} \\ \text{for }f\mleft(x\mright)=2^x\text{ : 2, 4} \end{gathered}$

See explanation and graph below

Explanation:

For x less than or equal to zero, we would apply the function f(x) = (1/2)^x

For x greater than zero, we would apply the function f(x) = 2^x

when x = - 2 (less than 0)

This falls in the 1st function

$\begin{gathered} f(-2)\text{ = (}\frac{1}{2})^{-2} \\ f(-2)=\frac{1}{(\frac{1}{2})^2}\text{ = 1}\times\frac{4}{1} \\ f(-2)=2^2\text{ = 4} \end{gathered}$

when x = -1 (less than 0)

This falls in the 1st function

$\begin{gathered} f(-1)\text{ = (}\frac{1}{2})^{-1} \\ f(-1)\text{ = }\frac{1}{(\frac{1}{2})^1}\text{ = 2} \end{gathered}$

when x = 0 (equal to 0)

This falls in the 1st function

$\begin{gathered} f(0)\text{ = (}\frac{1}{2})^0 \\ f(0)\text{ = 1} \end{gathered}$

when x = 1 (greater than 0)

This falls in the 2nd function

$\begin{gathered} f(1)=2^1 \\ f(1)\text{ = 2} \end{gathered}$

when x = 2 (greater than 0)

THis falls in the 2nd function

$\begin{gathered} f(2)\text{ = }2^2 \\ f(2)\text{ = 4} \end{gathered}$

Plotting the graph:

The end with the shaded dot reresent the function with equal to sign attached to the inequality [f(x) = (1/2)^x].

The end with the open dot represent the function without the equal to sign [f(x) = 2^x)