Question

graph the function f(x) = 3(2)^x by hand. then use a graphing calculator to verify your graph.
choose the correct graph below.
a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Analyze the function

The function is \( f(x) = 3(2)^x \), which is an exponential function. Exponential functions of the form \( f(x)=a(b)^x \) (where \( a>0, b > 1\)) are increasing functions. Here, \( a = 3\) and \( b=2>1\), so the function should be an increasing exponential curve. Also, when \( x = 0\), \( f(0)=3(2)^0=3\times1 = 3\), so the y - intercept is at \( (0,3)\).

Step2: Analyze the graphs

• For graph A: If it's a decreasing curve or has a different y - intercept, it's incorrect.
• For graph B: Check the y - intercept. If when \( x = 0\), the value is 3, and the curve is increasing (since \( b = 2>1\)), this graph should match.
• For graph C: If the y - intercept or the shape (increasing/decreasing) is wrong, it's incorrect.
• For graph D: If the y - intercept or the shape is wrong, it's incorrect.

Since the function \( f(x)=3(2)^x\) is an increasing exponential function with y - intercept at \( (0,3)\), we look for the graph that has these properties.

Answer:

B (assuming graph B has a y - intercept of 3 and is an increasing exponential curve)