Question

1. graph y = 7^x.

Explanation:

Step1: Find the y - intercept

When \(x = 0\), \(y=7^{0}=1\). So the graph passes through the point \((0,1)\).

Step2: Find other points

When \(x = 1\), \(y = 7^{1}=7\), the point is \((1,7)\); when \(x=- 1\), \(y = 7^{-1}=\frac{1}{7}\), the point is \((-1,\frac{1}{7})\).

Step3: Analyze the behavior

Since the base \(a = 7>1\), the function \(y = 7^{x}\) is an exponential - growth function. As \(x\to+\infty\), \(y\to+\infty\); as \(x\to-\infty\), \(y\to0\).

Step4: Plot the points and draw the graph

Plot the points \((0,1)\), \((1,7)\), \((-1,\frac{1}{7})\) on the coordinate - plane and draw a smooth curve passing through these points, which increases rapidly as \(x\) increases and approaches the \(x\) - axis as \(x\) decreases.

Answer:

The graph of \(y = 7^{x}\) is an exponential - growth curve passing through \((0,1)\), increasing as \(x\) increases and approaching the \(x\) - axis as \(x\) decreases.