Problem preview

F-IF.7.e Warmup M1-026-A07-V03

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

Match an exponential equation to graph features

Problem

Analyze \(y=-2\cdot~3^{x}\).

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asymptote y=0 approached from above; range (0,∞)

behavior = increasing because base 3>1; range positive

intercept (0,2); asymptote y=-2

y-intercept = (0,-2) because -2·3⁰=-2; behavior = decreasing because 3ˣ increases and multiplication by -2 reflects it across the x-axis; asymptote = y=0 approached from below as x→-∞; domain = (-∞,∞); range = (-∞,0)

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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: Match an exponential equation to graph features