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

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.

Table of contents

Skip topic navigation

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
  1h 16m
5. Applications of Derivatives2h 19m
6. Graphical Applications of Derivatives6h 0m
7. Antiderivatives & Indefinite Integrals48m
- Antiderivatives
  17m
- Indefinite Integrals
  31m
8. Definite Integrals4h 36m
9. Graphical Applications of Integrals1h 43m
- Area Between Curves
  1h 19m
- Introduction to Volume & Disk Method
  23m
10. Integrals of Inverse, Exponential, & Logarithmic Functions21m
- Integrals of Exponential Functions
  14m
- Integrals Involving Logarithmic Functions
  7m
11. Techniques of Integration2h 7m
- Integration by Parts
  1h 37m
- Improper Integrals
  29m
12. Trigonometric Functions6h 54m
13: Intro to Differential Equations2h 23m
14. Sequences & Series2h 8m
15. Power Series2h 19m
- Power Series & Taylor Series
  2h 19m
16. Probability & Calculus45m
- Continuous Probability Models
  45m

0. Functions

Piecewise Functions

Business Calculus

0. Functions

Piecewise Functions

Previous problemNext problem

Struggling with Business Calculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

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

$130$

$125$

$120$

$30$

Previous problemNext problem

Verified step by step guidance

Step 1: Analyze the piecewise function provided. The function is defined in three parts: (1) f(x) = 2x + 4 for x < 0, (2) f(x) = x^2 for 0 ≤ x < 2, and (3) f(x) = x^3 + 5 for x ≥ 2.

Step 2: Determine which part of the piecewise function applies to the given input x = 5. Since 5 is greater than or equal to 2, the third part of the function, f(x) = x^3 + 5, is applicable.

Step 3: Substitute x = 5 into the applicable part of the function, f(x) = x^3 + 5. This means you will calculate 5^3 + 5.

Step 4: Simplify the expression 5^3 + 5. First, calculate 5^3 (which is 5 multiplied by itself three times), then add 5 to the result.

Step 5: The simplified result will give you the value of f(5).