Graph the function f(x) = 5(0.21)x.
To graph the function f(x) = 5(0.21)x, we can follow these steps:
Step 1: Identify the base and coefficient:
The given function can be rewritten in the form f(x) = a(b)x, where a = 5 and b = 0.21. The base, b, indicates the multiplicative factor by which the value of the function changes for each unit change in x. The coefficient, a, is a constant that affects the vertical scale of the graph.
Step 2: Choose some values for x:
To plot the graph, we need to choose a few values for x. Let's select a range of x-values to showcase the behavior of the function. For example, we can take x = -2, -1, 0, 1, 2.
Step 3: Calculate f(x) for the chosen x-values:
Plug in the chosen x-values into the function f(x) = 5(0.21)x to find the corresponding y-values. For example,
f(-2) = 5(0.21)^-2
f(-1) = 5(0.21)^-1
f(0) = 5(0.21)^0
f(1) = 5(0.21)^1
f(2) = 5(0.21)^2
Step 4: Plot the points:
Using the calculated x and y-values, plot the points (-2, f(-2)), (-1, f(-1)), (0, f(0)), (1, f(1)), (2, f(2)) on a graph.
Step 5: Connect the points:
Draw a smooth curve that passes through the plotted points. Since the function is exponential, the resulting curve should be increasing or decreasing exponentially, depending on the value of the base.
Step 6: Label the axes and add a title:
Label the horizontal axis as x and the vertical axis as f(x). Add a title to the graph, for example, "Graph of f(x) = 5(0.21)^x."
By following these steps, you can create a graph of the function f(x) = 5(0.21)x.
To graph the function f(x) = 5(0.21)x, we can follow these steps:
Step 1: Decide on the range of x-values you want to plot. For simplicity, let's choose a few values for x, such as -3, -2, -1, 0, 1, 2, and 3.
Step 2: Evaluate the function at each chosen x-value. Plug in each value of x into the function f(x) = 5(0.21)x and calculate the corresponding y-value.
For example:
When x = -3, f(-3) = 5(0.21)-3 = 5(0.21)-3 = 5(0.00407407407) ≈ 0.02037037037
When x = -2, f(-2) = 5(0.21)-2 = 5(0.21)-2 = 5(0.042) = 0.21
When x = -1, f(-1) = 5(0.21)-1 = 5(0.21)-1 = 5(0.084) = 0.42
When x = 0, f(0) = 5(0.21)0 = 5(1) = 5
When x = 1, f(1) = 5(0.21)1 = 5(0.21) = 1.05
When x = 2, f(2) = 5(0.21)2 = 5(0.441) = 2.205
When x = 3, f(3) = 5(0.21)3 = 5(0.9261) = 4.6305
Step 3: Plot the points (x, y) for each calculated value. On a graph with x and y axes, plot the points (-3, 0.02037037037), (-2, 0.21), (-1, 0.42), (0, 5), (1, 1.05), (2, 2.205), and (3, 4.6305).
Step 4: Connect the plotted points with a smooth curve. Since the function is an exponential function, the graph should gradually increase or decrease depending on the value of x.
Step 5: Label the axes and provide a suitable title for the graph.
That's it! You have now graphed the function f(x) = 5(0.21)x.
I assume you are working with an exponential function
f(x) = 5 * 0.21^x
All functions y = a^x go through the point (0,1)
so, clearly, yours must go through (0,5)
Now, when x=1, y = 5*0.21 = 1.05
Having reviewed the topic in your text, or online, you should now be able to sketch the curve. Just to make things easy, all exponential functions look basically the same. Just draw a typical curve, then label the axes appropriately.