Question

Evaluate this function at x=1. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".

Answer 1

@tranquility

Answer 2

Hi! In order to work this problem, it seems much easier than it is. A piecewise function is just this math term created because mathmaticians always want to make homework hard. it's basically two or more functions that have restricted domains that are usually continuous combined.
When you want to figure out f(1), it basically means, at x=1, what number is equal to that? We can use some common sense. The first function says that the domain restricts at -3, which means that that specific function ends off at x=-3. We see that the function continues off with that different one, the second one. The second one states that the domain is greater than or equal to -3, which means that after x=-3, the line is that function. Aside from this blah blah blah, the second function is the one you should focus on since you're trying to find x=1.
(hint: plug in 1 for the second equation to get the solution.)

Answer 3

\[\frac{ 1 }{ 2} x + 5 \] if \[x \ge -3\]

Answer 4

Yes, correct! Substitute 1 for x to get the proper answer for f(1).

Answer 5

d\[-\frac{ 1 }{ 2} (-3) + 5 = \frac{ 13 }{ 2}\]

Answer 6

Where did you get -3 from?

Answer 7

-3 is solely there to restrict the domain. it just means that after the x value -3, it continues as this line rather than the line before.

Answer 8

i looked at both functions to see where x can equal -3. only the second function alloed it

Answer 9

allowed

Answer 10

Since the problem is saying to find x=1, plug in 1.

Answer 11

\[-\frac{ 1 }{ 2}(1) + 5 = \frac{ 9 }{ 2}\]

Answer 12

What is this negative sign from?

Answer 13

oh sorry

Answer 14

\[\frac{ 1 }{ 2}(1) + 5 = \frac{ 11 }{ 2 }\]

Answer 15

No worries, never apologize. yes, that is the correct answer.

Answer 16

thank you, could you help me with more or you're available some time

Answer 17

it's the same question but it says Evaluate this function at x=−3. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".

Answer 18

New post please