The table when completed looks like this:
x -2 -1 0 1 2
f(x) 4 2 1 2 4.
The graph is provided in the attachment.
What is a function?
A function is a relation between a dependent variable (say f(x) ) and an expression of an independent variable (say x), used to determine the value of a dependent variable from a given value of an independent variable.
How do we solve the given question?
We have been given a function,
[tex]f(x) = \left \{ {{\frac{1}{2}^{x} , x \leq 0} \atop {2^{x}, x > 0 }} \right.[/tex]
We are asked to determine the value of f(x) when x = {-2, -1, 0, 1, 2}
For the values of x ≤ 0, we will take f(x) = (1/2)ˣ.
∴ f(-2) = (1/2)⁻² = 2² = 4
f(-1) = (1/2)⁻¹ = 2¹ = 2
f(0) = (1/2)⁰ = 1
Now, for the values of x > 0, we take f(x) = 2ˣ
∴ f(1) = 2¹ = 2
f(2) = 2² = 4
We can design the table now as
x -2 -1 0 1 2
f(x) 4 2 1 2 4.
We plot these points on the graph: (-2, 4), (-1, 2), (0, 1), (1, 2), (2, 4).
The graph is attached.
Learn more about Functions at
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