Question

Y=2n+3 ; Find h(-2)
Answer should be -1

Answer 1

Why do you do H(n) at the beginning and not y?

Answer 2

Also when you did h(-2) = 2(-2) + 3
How did you get ( 2(-2) = -4 ?

Answer 3

To find \( h(-2) \) based on the equation you provided, we first need to clarify what \( Y \) represents. If \( Y = 2n + 3 \) represents a function \( h(n) \), then we can rewrite it as:

\[
h(n) = 2n + 3
\]

Now, we will substitute \( n = -2 \) into this function:

\[
h(-2) = 2(-2) + 3
\]

Calculating this step-by-step:

1. \( 2(-2) = -4 \)
2. Now add 3: \( -4 + 3 = -1 \)

So,

\[
h(-2) = -1
\]

Thus, the value of \( h(-2) \) is indeed \(-1\).

Answer 4

I used \( h(n) \) instead of \( Y \) as a way to define the function more clearly in the context of finding a specific value, \( h(-2) \). If \( Y = 2n + 3 \), we can simply treat \( Y \) as a function named \( h(n) \) for clarity.

Here's the breakdown:

1. **Defining the Function**: The equation \( Y = 2n + 3 \) can be interpreted as a function where:
- \( Y \) is the output,
- \( n \) is the input.

To represent this more conventionally, we can write it as \( h(n) = 2n + 3 \).

2. **Finding a Specific Value**: When you wanted to find \( h(-2) \), using \( h(n) \) helps to explicitly indicate that we are evaluating the function at \( n = -2 \).

3. **Consistency**: It’s common in mathematics to define a function using a different letter (like \( h \)) for convenience or clarity, especially when evaluating specific values.

Regardless of whether we call it \( Y \) or \( h(n) \), the mathematical reasoning remains the same. The outcome is the same:

\[
h(-2) = 2(-2) + 3 = -4 + 3 = -1
\]

In summary, both \( Y \) and \( h(n) \) serve the same purpose in this context, but using \( h(n) \) can help clarify that we're dealing with a function.

Answer 5

When calculating \( 2(-2) \), you're multiplying \( 2 \) by \( -2 \). Here’s how that works:

1. **Multiplication of a Positive and a Negative Number**: When you multiply a positive number by a negative number, the result is negative. In this case, you are multiplying \( 2 \) (a positive number) by \( -2 \) (a negative number).

2. **Performing the Calculation**:
\[
2 \times -2 = -4
\]

So, \( 2(-2) \) simplifies to \( -4 \).

Putting this back into the equation:

\[
h(-2) = 2(-2) + 3 \rightarrow h(-2) = -4 + 3 = -1
\]

Thus, that step \( 2(-2) = -4 \) is based on the rule that a positive times a negative equals a negative. Let me know if you need further clarification!