Problem preview

F-IF.7.e Warmup M1-026-A02-V03

Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.

Graph an exponential decay function

Problem

Graph \(h(x)~=~9\cdot~(1/3)^{x}\) on the grid. State the initial value, retained factor and decay percent, verified points and ratio, horizontal asymptote, domain, and range.

Blank coordinate grid tailored to plotting h(x)=9·(1/3)ˣ, without a completed curve or derived features.

Answer choices

Choose your path.

Preview only

initial 1/3; factor 9; points 1/3,3,27

initial = h(0)=9; retained factor = 1/3; decay percent = 66⅔% per +1 input; points = (0,9),(1,3),(2,1); ratio check = 3/9=1/3 and 1/3=1/3; asymptote = y=0; domain = (-∞,∞); range = (0,∞)

factor 3; growth 200%; points 9,27,81

retained factor 1/3; decay percent 33⅓%; points 9,6,4

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Inside Gozunta

Turn the preview into practice.

More than a preview

Gozunta lets you study this problem—and more than 10,000 others.

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now

Curriculum context

Course: Math I
Standard: F-IF.7.e
Category: Functions
Domain: Interpreting Functions
Objective: Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.
Problem type: Graph an exponential decay function