Questions: Graph the exponential function (y=7^x).

Transcript text: Graph the exponential function $\boldsymbol{y}=7^{x}$.

Solution

Step 1: Identify the Exponential Function

The given exponential function is $ y = 7^x $.

Step 2: Understand the Characteristics of the Function

An exponential function of the form $ y = a^x $ (where $ a > 1 $) has the following characteristics:

It passes through the point (0,1) because any number to the power of 0 is 1.
It increases rapidly as $ x $ increases.
It approaches 0 as $ x $ decreases but never actually reaches 0 (asymptote at $ y = 0 $).

Step 3: Analyze the Graphs

The first graph shows a function that decreases as $ x $ increases, which is not characteristic of $ y = 7^x $.
The second graph shows a function that decreases as $ x $ increases, which is also not characteristic of $ y = 7^x $.
The third graph shows a function that increases as $ x $ increases and passes through the point (0,1), which matches the characteristics of $ y = 7^x $.

The correct graph for the exponential function $ y = 7^x $ is the third graph.

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