Question

Determine f(−2) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4.

Answer 1

Answer: -1

Step-by-step explanation:

Answer 2

Answer: -1

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Step-by-step explanation:

This is the given piecewise function

`f(\text{x}) = \begin{cases}\text{x}^3 \ \ \ \ \ \ \ \ \text{ if } \text{x} < -3\\2\text{x}^2-9 \ \text{ if } -3 \le \text{x} < 4\\5\text{x}+4 \ \ \text{ if } \text{x} \ge 4\\\end{cases}`

This is another way to look at the piecewise function

• If
  `\text{x} < -3`, then
  `f(\text{x}) = \text{x}^3`
• If
  `-3 \le \text{x} < 4`, then
  `f(\text{x}) = 2\text{x}^2-9`
• If
  `\text{x} \ge 4`, then
  `f(\text{x}) = 5\text{x}+4`

We have 3 different branches or pathways to take based on what the x input is.

We want to compute f(-2). This means we want to find f(x) when x = -2 is the input.

This input matches with the interval
`-3 \le \text{x} < 4` since
`-3 \le -2 < 4` is a true statement. Therefore, we'll use the second option

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Plug x = -2 into the second part to get...

`f(\text{x}) = 2\text{x}^2-9 \ \ \text{ when } -3 \le \text{x} < 4\\\\f(-2) = 2(-2)^2-9 \\\\f(-2) = 2(4)-9 \\\\f(-2) = 8-9 \\\\f(-2) = -1 \\\\`