Using the piecewise function below, evaluate f ( − 1 ) f\left(-1\right) f ( − 1 )

take a look at this problem. Here, we're told using the piecewise function below, evaluate f of negative one. Now notice that we have this piecewise function where there are 3 pieces to the function here. We have this section where x is less than 3, this section where x is between 38. It could be equal to 3, but it can't be equal to 8. And then we have the situation where x is either greater than or equal to 8 for this function right here, this equation. So how exactly do we evaluate this? Well, what we need to do is figure out where negative one falls in these restrictions we have right here. So is negative one greater than or equal to 8? Well, no. It's not. It's quite a bit less than 8. So is it gonna be between 38? Well, it's also not there. We can see the only place where negative one exists is going to be in this place where x is less than 3, because negative one is obviously less than 3. So this would be the output for our function for negative one. So that means f of negative one is going to be this constant that we see right here, which is 4. There's no x's in here, so we don't have to plug that in, meaning that all we have is 4 as our answer. Hope you found this video helpful.

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0. Functions4h 53m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation2h 18m
4. Derivatives of Exponential & Logarithmic Functions1h 16m
- Derivatives of Exponential & Logarithmic Functions
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5. Applications of Derivatives2h 19m
6. Graphical Applications of Derivatives6h 0m
7. Antiderivatives & Indefinite Integrals48m
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8. Definite Integrals4h 36m
9. Graphical Applications of Integrals1h 43m
- Area Between Curves
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- Introduction to Volume & Disk Method
  23m
10. Integrals of Inverse, Exponential, & Logarithmic Functions21m
- Integrals of Exponential Functions
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11. Techniques of Integration2h 7m
- Integration by Parts
  1h 37m
- Improper Integrals
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12. Trigonometric Functions6h 54m
13: Intro to Differential Equations2h 23m
14. Sequences & Series2h 8m
15. Power Series2h 19m
- Power Series & Taylor Series
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16. Probability & Calculus45m
- Continuous Probability Models
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0. Functions

Piecewise Functions

Business Calculus

0. Functions

Piecewise Functions

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Multiple Choice

Using the piecewise function below, evaluate $f\left(-1\right)$

$-4$

$4$

$\pm \sqrt{3}$

$2$

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Verified step by step guidance

Step 1: Understand the piecewise function provided. The function f(x) is defined in three parts: f(x) = 4 if x < 3, f(x) = x^2 - 3 if 3 ≤ x < 8, and f(x) = x^3 if x ≥ 8.

Step 2: Determine which part of the piecewise function applies to the input x = -1. Since -1 is less than 3, the first part of the function f(x) = 4 is applicable.

Step 3: Substitute x = -1 into the applicable part of the function. Since the function is constant (f(x) = 4) for x < 3, the value of f(-1) is directly 4.

Step 4: Verify the result by checking the conditions of the piecewise function. Confirm that -1 satisfies the condition x < 3, so the correct part of the function was used.

Step 5: Conclude that the evaluation of f(-1) is complete using the piecewise function, and the result is determined by the constant value in the first part of the function.