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. Functions7h 52m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation3h 18m
4. Applications of Derivatives2h 38m
5. Graphical Applications of Derivatives6h 2m
6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
7. Antiderivatives & Indefinite Integrals1h 26m
8. Definite Integrals4h 44m
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- Area Between Curves
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- Introduction to Volume & Disk Method
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10. Physics Applications of Integrals 3h 16m
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- Work
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11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
12. Techniques of Integration7h 39m
13. Intro to Differential Equations2h 55m
14. Sequences & Series5h 36m
15. Power Series2h 19m
- Introduction to Power Series
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- Taylor Series & Taylor Polynomials
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16. Parametric Equations & Polar Coordinates7h 58m

0. Functions

Piecewise Functions

Calculus

0. Functions

Piecewise Functions

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Multiple Choice

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

$negative 4$

$4$

$\pm \sqrt{3}$

$2$

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Verified step by step guidance

First, identify the piecewise function given in the image. The function f(x) is defined as follows: f(x) = 4 if x < 3, f(x) = x^2 - 3 if 3 ≤ x < 8, and f(x) = x^3 if x ≥ 8.

Determine which piece of the function to use for evaluating f(-1). Since -1 is less than 3, we use the first piece of the function, which is f(x) = 4.

Substitute x = -1 into the first piece of the function. Since this piece is a constant function, f(-1) = 4.

The evaluation of f(-1) using the piecewise function is straightforward because it falls into the range where the function is constant.

Thus, the value of f(-1) is 4, according to the piecewise definition provided.