Questions: Graph the exponential function. f(x)=-3^x Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Graph the exponential function.
f(x)=-3^x

Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Transcript text: Graph the exponential function. \[ f(x)=-3^{x} \] Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Solution

Solution Steps

Step 1: Identify the Function

The given function is \( f(x) = -3^x \).

Step 2: Determine Key Points

To plot the graph, we need to determine five key points. We can choose values for \( x \) and calculate the corresponding \( y \) values:

For \( x = -2 \): \( f(-2) = -3^{-2} = -\frac{1}{9} \)
For \( x = -1 \): \( f(-1) = -3^{-1} = -\frac{1}{3} \)
For \( x = 0 \): \( f(0) = -3^0 = -1 \)
For \( x = 1 \): \( f(1) = -3^1 = -3 \)
For \( x = 2 \): \( f(2) = -3^2 = -9 \)

Step 3: Plot the Points

Plot the points \((-2, -\frac{1}{9})\), \((-1, -\frac{1}{3})\), \((0, -1)\), \((1, -3)\), and \((2, -9)\) on the graph.

Step 4: Draw the Asymptote

The horizontal asymptote for the function \( f(x) = -3^x \) is \( y = 0 \).

Final Answer

The points to plot are \((-2, -\frac{1}{9})\), \((-1, -\frac{1}{3})\), \((0, -1)\), \((1, -3)\), and \((2, -9)\).
The horizontal asymptote is \( y = 0 \).

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