# Determine the value of a for a given function.

• Torshi
In summary, in order to determine the value of "a" for the given function, you must solve for "a" such that the left-side limit as x approaches 2 is equal to 8. This can be done by setting the left-side limit as 2a+7 and the right-side limit as 8-a, and solving for "a". The solution is a = 1/2.
Torshi
Determine the value of "a" for a given function.

## Homework Statement

Consider the following function: f(x) { ax+7, x<2 and 4x-a, x≥2

A.) Determine the value of "a" such that lim x->2- (approaching from left) f(x) = 8. You mus demonstrate all limits.

## Homework Equations

ax+7, x<2 and 4x-a, x≥2

## The Attempt at a Solution

Approaching from left I got lim x->2- (2a+7) and from right lim x->2+ (8-a)
Am I trying to find a? If I set both limits equal I get a = .33, but the question asks determine the value of such that lim x->2- f(x) = 8 ? That would mean a =1/2 because 2* 1/2 = 1 + 7 = 8, but I don't think that's right unless I'm reading the question wrong..

Edit:
Or do I just state that ax+7 since for this question says lim x->2- (approaching) left f(x) = 8 do I say coming from the left is 8 while from the right it's still 8-a then set those two equal to calculate for "a"? Getting -1 as my answer for "a"?

Last edited:

Torshi said:

## Homework Statement

Consider the following function: f(x) { ax+7, x<2 and 4x-a, x≥2

A.) Determine the value of "a" such that lim x->2- (approaching from left) f(x) = 8. You mus demonstrate all limits.

## Homework Equations

ax+7, x<2 and 4x-a, x≥2

## The Attempt at a Solution

Approaching from left I got lim x->2- (2a+7) and from right lim x->2+ (8-a)
This is what you mean:
$$\lim_{x \to 2^-}f(x) = 2a + 7$$
$$\lim_{x \to 2^+}f(x) = 8 - a$$
Torshi said:
Am I trying to find a?
Yes, so that the left-sided limit as x approaches 2 equals 8.
Torshi said:
If I set both limits equal I get a = .33, but the question asks determine the value of such that lim x->2- f(x) = 8 ? That would mean a =1/2 because 2* 1/2 = 1 + 7 = 8
What are you saying here? 2 * 1/2 = 1 ≠ 8
Torshi said:
, but I don't think that's right unless I'm reading the question wrong..

Edit:
Or do I just state that ax+7 since for this question says lim x->2- (approaching) left f(x) = 8 do I say coming from the left is 8 while from the right it's still 8-a then set those two equal to calculate for "a"? Getting -1 as my answer for "a"?

Mark44 said:
This is what you mean:
$$\lim_{x \to 2^-}f(x) = 2a + 7$$
$$\lim_{x \to 2^+}f(x) = 8 - a$$
Yes, so that the left-sided limit as x approaches 2 equals 8.

Alright, then now I'm assuming set 8 = 8-a

Torshi said:
Alright, then now I'm assuming set 8 = 8-a --> which equals a = -1. Thanks
No, for two reasons.

1) You are supposed to
Determine the value of "a" such that lim x->2- (approaching from left) f(x) = 8
2)If 8 = 8 - a, then a = -1 is NOT the solution.

For the left-side limit, a = 1/2.
You had that, but wrote something that didn't make sense.

If a = 1/2, then 2a + 7 = 2(1/2) + 7 = 8

Mark44 said:
No, for two reasons.

1) You are supposed to
2)If 8 = 8 - a, then a = -1 is NOT the solution.
Sorry, i realized that I switched it to a-8 for some odd reason. Nevermind, I don't know how I came up with that. My fault.

8 = 8 - a
a+8 = 8
a = 0
?

The question is asking about the left-side limit, not the right-side limit.

Mark44 said:
The question is asking about the left-side limit, not the right-side limit.

Wait, but I thought the question said to determine the value of "a" such that lim x->2- f(x) = 8 meaning that approaching from the left lim x->2- = 8 and from the right that being 8-a, we solve for "a" which is from lim x->2+ (8-a) , so 8 = 8-aif it's the other way around a = 1/2

Last edited:

I think I get it.

2a+7 = 8 then solve for a

a = 1/2

Thanks

Mark44 said:
For the left-side limit, a = 1/2.
You had that, but wrote something that didn't make sense.

If a = 1/2, then 2a + 7 = 2(1/2) + 7 = 8

I did say that, but I said it without solving so it was just an assumption by looking at the problem, the reason why I didn't go with it because it sounded too easy even though it made sense. My fault. Thank you.

## 1. What is the purpose of determining the value of a for a given function?

The value of a in a function represents the coefficient or constant that affects the shape and position of the graph. It allows us to make predictions and understand the behavior of the function.

## 2. How do you determine the value of a for a linear function?

For a linear function in the form y = mx + b, a represents the slope or rate of change. It can be calculated by dividing the change in y values by the corresponding change in x values between two points on the graph.

## 3. What is the significance of determining the value of a for a quadratic function?

In a quadratic function, a represents the coefficient of the squared term. This value determines the shape of the parabola and can give information about the maximum or minimum point of the function.

## 4. Can the value of a for a given function change?

Yes, the value of a can vary depending on the specific function and its parameters. It can also be manipulated by applying transformations to the original function.

## 5. How can determining the value of a for a given function be applied in real-world situations?

In many fields of science, such as physics and engineering, functions are used to model real-world phenomena. By determining the value of a, we can make predictions and solve problems related to these phenomena.

• Calculus and Beyond Homework Help
Replies
3
Views
835
• Calculus and Beyond Homework Help
Replies
1
Views
446
• Calculus and Beyond Homework Help
Replies
2
Views
824
• Calculus and Beyond Homework Help
Replies
4
Views
842
• Calculus and Beyond Homework Help
Replies
4
Views
521
• Calculus and Beyond Homework Help
Replies
2
Views
584
• Calculus and Beyond Homework Help
Replies
7
Views
862
• Calculus and Beyond Homework Help
Replies
30
Views
2K
• Calculus and Beyond Homework Help
Replies
2
Views
618
• Calculus and Beyond Homework Help
Replies
2
Views
764