Final answer:
To graph f(x) = 2^x, plot points with two negative, zero, and two positive x-values. Then, for g(x) = 2(2)^-1/3 * (x+2) - 5, apply transformations to these points: horizontal shift, scale and reflection, and vertical shift. Plot the transformed points to complete the graph.
Step-by-step explanation:
To draw a graph of the function f(x) = 2^x, we need to create a table of values. We will include two negative values for x, zero, and two positive values for x. Here's an example table:
- x = -2, f(x) = 2² = 0.25
- x = -1, f(x) = 2²= 0.5
- x = 0, f(x) = 2² = 1
- x = 1, f(x) = 2² = 2
- x = 2, f(x) = 2² = 4
Plot these points on a graph with the x-values on the horizontal axis and the f(x) values on the vertical axis. The graph will show an exponential growth pattern.
For the function g(x) = 2(2)^-1/3 * (x+2) - 5, apply transformations to the points found in part (a). There are three steps in the transformation:
- Horizontal shift: Replace x with (x + 2).
- Scale and reflect: Multiply the f(x) by 2 and then by (2)^-1/3.
- Vertical shift: Subtract 5 from the result.
Once the points are transformed, plot them on the graph to get the desired function g(x).
The complete queston is: Using a table of values draw a graph of the function f(x)=2ˣ. In your table of values, you mustindude two negative values for x, zero, and two positive values for x.b. Do transformations on the points that you found in part (a) to draw a graph of the functionbelowg(x)= 2(2)⁻¹/3(x+2) - 5 is: