Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Type the correct answer in each box. Use numerals instead of words.

Consider the function \( h \):
[tex]\[
h(x) =
\begin{cases}
3x - 4, & x \ \textless \ 0 \\
2x^2 - 3x + 10, & 0 \leq x \ \textless \ 4 \\
2^x, & x \geq 4
\end{cases}
\][/tex]

What are the values of the function when \( x = 0 \) and when \( x = 4 \)?
[tex]\[
\begin{array}{l}
h(0) = \square \\
h(4) = \square
\end{array}
\][/tex]

Sagot :

GinnyAnswer
Let's evaluate the function \( h(x) \) at the specified points \( x = 0 \) and \( x = 4 \).

1. Evaluating \( h(0) \):

According to the piecewise function definition, when \( 0 \leq x < 4 \), we use the formula:
[tex]\[ h(x) = 2x^2 - 3x + 10 \][/tex]

For \( x = 0 \):
[tex]\[ h(0) = 2(0)^2 - 3(0) + 10 = 0 - 0 + 10 = 10 \][/tex]

2. Evaluating \( h(4) \):

According to the piecewise function definition, when \( x \geq 4 \), we use the formula:
[tex]\[ h(x) = 2^x \][/tex]

For \( x = 4 \):
[tex]\[ h(4) = 2^4 = 16 \][/tex]

Thus, the values of the function are:
[tex]\[ h(0) = 10 \][/tex]
[tex]\[ h(4) = 16 \][/tex]
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.