Question

which of the following is not a correct step for graphing an exponential function?
a. plot two points and connect them with a curve without finding the y-intercept.
b. plot several points using values of x on a table.
c. determine if the function represents growth or decay based on the base value.
d. identify the horizontal asymptote.

Explanation:

To determine the incorrect step for graphing an exponential function, we analyze each option:

• Option b: Plotting several points using \( x \)-values in a table is a standard step to graph functions, including exponential ones, as it helps visualize the curve.
• Option c: Determining growth or decay (based on if the base \( b \) of \( y = a b^x \) is \( b>1 \) (growth) or \( 0 < b < 1 \) (decay)) is essential to understand the function's behavior.
• Option d: Identifying the horizontal asymptote (e.g., \( y = 0 \) for \( y = a b^x \) when \( a

eq0 \)) is a key step in graphing exponential functions to show the end - behavior.

• Option a: Exponential functions have a y - intercept (when \( x = 0 \), \( y=a \) for \( y = a b^x \)). Plotting only two points without considering the y - intercept (or other key features) is not a correct step, as it may lead to an inaccurate graph.

Answer:

a. Plot two points and connect them with a curve without finding the y - intercept.