Piecewise Function Evaluation for Different Values of x

Math Problem Statement

Evaluate the function f(x) = {7x + 1, x < -1; x^3 - 3, x >= -1} for x = 5, x = -1, x = 0, x = -2, and x = 1.

Let's solve the problems shown in the image. The given piecewise function is:

7x + 1 & \text{if } x < -1 \\ x^3 - 3 & \text{if } x \geq -1 \end{cases}$$ We need to evaluate the function for the given values of $$x$$. 1. **Evaluate the function for $$x = 5$$:** Since $$x = 5 \geq -1$$, we use the second part of the function: $$f(5) = 5^3 - 3 = 125 - 3 = 122$$ 2. **Evaluate the function for $$x = -1$$:** Since $$x = -1 \geq -1$$, we use the second part of the function: $$f(-1) = (-1)^3 - 3 = -1 - 3 = -4$$ 3. **Evaluate the function for $$x = 0$$:** Since $$x = 0 \geq -1$$, we use the second part of the function: $$f(0) = 0^3 - 3 = 0 - 3 = -3$$ 4. **Evaluate the function for $$x = -2$$:** Since $$x = -2 < -1$$, we use the first part of the function: $$f(-2) = 7(-2) + 1 = -14 + 1 = -13$$ 5. **Evaluate the function for $$x = 1$$:** Since $$x = 1 \geq -1$$, we use the second part of the function: $$f(1) = 1^3 - 3 = 1 - 3 = -2$$ Here's a summary of the evaluations: - $$f(5) = 122$$ - $$f(-1) = -4$$ - $$f(0) = -3$$ - $$f(-2) = -13$$ - $$f(1) = -2$$ Would you like details or have any questions about these evaluations? Here are five related questions for further practice: 1. Evaluate the function for $$x = -3$$. 2. Evaluate the function for $$x = 2$$. 3. What is the value of $$f(x)$$ when $$x = -0.5$$? 4. For what values of $$x$$ is $$f(x) = 0$$? 5. Determine the intervals where $$f(x)$$ is increasing. **Tip:** When dealing with piecewise functions, always check the condition for the value of $$x$$ to determine which part of the function to use.

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Piecewise Functions
Algebra
Polynomial Functions

f(x) = 7x + 1, if x < -1
f(x) = x^3 - 3, if x >= -1

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