Using the piecewise function below, evaluate f ( 5 ) f\left(5\right)

Using the piecewise function that we're given right here, we're asked to evaluate f of 5. Now notice here that we have these restrictions for our piecewise function. These are, in essence, these walls that show up in our function where we have these certain places where we have one curve for this piece, then we'll have another curve for that piece, then another curve for this piece. We talked about that when we discussed piecewise functions. And we need to figure out which piece this 5 here falls into. Well, if we look at that, 5 is clearly not less than 0. So we can rule out this function right here, this part of the the function, I should say. We can also see that 5 is clearly not between 0 and 2. 5 is greater than 2, so it does not fall within this this values right here. So what that means is the only option we have left is this situation where x is greater than or equal to 2. 5 is greater than or equal to 2. It's greater than 2, so that means this is the function we're going to be using. So if we want to evaluate f of 5, well, in this case, we're going to just plug 5 in for the x in this equation. It's going to be 5 cubed plus 5. Now 5 cubed, that's going to be 5 times 5, which is 25 times another 5, which is a 125. Then you add that to the 5 we have on the end there, it's gonna give you a 130. So 130 is the answer to this problem. Let's go ahead and move on.

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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
9. Graphical Applications of Integrals2h 27m
- Area Between Curves
  1h 18m
- Introduction to Volume & Disk Method
  1h 8m
10. Physics Applications of Integrals 3h 16m
- Kinematics
  1h 13m
- Work
  2h 3m
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
  1h 9m
- Taylor Series & Taylor Polynomials
  1h 10m
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 $f of 5$

$130$

$125$

$120$

$30$

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Verified step by step guidance

Identify the piecewise function and the conditions for each piece. The function is defined as: f(x) = 2x + 4 if x < 0, f(x) = x^2 if 0 ≤ x < 2, and f(x) = x^3 + 5 if x ≥ 2.

Determine which condition applies to the value x = 5. Since 5 is greater than or equal to 2, we use the third piece of the function: f(x) = x^3 + 5.

Substitute x = 5 into the expression for the third piece of the function: f(5) = 5^3 + 5.

Calculate the value of 5^3. This involves multiplying 5 by itself three times.

Add 5 to the result of 5^3 to find the value of f(5).