19.03.2023 - 17:28

The figure shows the graphs of y = 2x, y = ex, y = 10x, y = 2-x, y = e-x, and y = 10-x. Match each function with its graph. The graphs are labeled (a) through (f). Explain your reasoning.

Question:

The figure shows the graphs of {eq}y={{2}}^{{x}} {/eq}, {eq}y={{e}}^{{x}} {/eq}, {eq}y={{10}}^{{x}} {/eq}, {eq}y={{2}}^{{-x}} {/eq}, {eq}y={{e}}^{{-x}} {/eq}, and , {eq}y={{10}}^{{-x}} {/eq} . Match each function with its graph. The graphs are labeled (a) through (f). Explain your reasoning.

Answers (1)
  • Gussie
    April 17, 2023 в 23:13
    (a) - {eq}y={{2}}^{{x}} {/eq} (b) - {eq}y={{e}}^{{x}} {/eq} (c) - {eq}y={{10}}^{{x}} {/eq} (d) - {eq}y={{2}}^{{-x}} {/eq} (e) - {eq}y={{e}}^{{-x}} {/eq} (f) - {eq}y={{10}}^{{-x}} {/eq} Reasoning: - The functions {eq}y={{2}}^{{x}} {/eq}, {eq}y={{e}}^{{x}} {/eq}, and {eq}y={{10}}^{{x}} {/eq} all have exponential growth, increasing rapidly as x increases, and their graphs increase from left to right. - The functions {eq}y={{2}}^{{-x}} {/eq}, {eq}y={{e}}^{{-x}} {/eq}, and {eq}y={{10}}^{{-x}} {/eq} all have exponential decay, decreasing rapidly as x increases, and their graphs decrease from left to right. - Based on the scale of the axes, we can see that the function with the fastest growth rate is {eq}y={{10}}^{{x}} {/eq}, while the function with the slowest growth rate is {eq}y={{2}}^{{x}} {/eq}. Similarly, the function with the fastest decay rate is {eq}y={{10}}^{{-x}} {/eq}, while the function with the slowest decay rate is {eq}y={{2}}^{{-x}} {/eq}. Using these observations, we can match each function with its graph as shown in the figure.
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