Question

what is a valid first step when graphing an exponential function?

a. find the x-intercept by solving for ( x = 0 ).

b. identify the vertical asymptote.

c. make a table of x- and y-values.

d. plot a few points and connect them with a straight line.

Explanation:

• Option a: To find the x - intercept, we solve for \(y = 0\), not \(x=0\) (solving \(x = 0\) gives the y - intercept). So this is incorrect.
• Option b: Exponential functions of the form \(y=a^x + k\) (\(a>0,a

eq1\)) have horizontal asymptotes (e.g., \(y = k\)), not vertical asymptotes. So this is incorrect.

• Option c: Making a table of x - and y - values is a valid first step when graphing an exponential function. We can choose values of \(x\) (like \(x=- 2,-1,0,1,2\)) and calculate the corresponding \(y\) values using the exponential function formula, then plot these points.
• Option d: Exponential functions are not linear, so we cannot connect the points with a straight line. The graph of an exponential function has a curve (either increasing or decreasing exponentially). So this is incorrect.

Answer:

c. Make a table of x - and y - values.