Math Problem Statement
For the indicated function, find the values f(negative 4), f(0), and f(7). f left parenthesis x right parenthesis equals StartSet Start 2 By 1 Matrix 1st Row 1st Column x comma if x less than 0 2nd Row 1st Column 5 x plus 8 comma if x greater than or equals 0 EndMatrix
Question content area bottom Part 1 f(negative 4)equals
enter your response here Part 2 f(0)equals
enter your response here Part 3 f(7)equals
enter your response here
Solution
To find the values of , , and for the given piecewise function, we will evaluate the function based on the conditions provided:
x, & \text{if } x < 0 \\ 5x + 8, & \text{if } x \geq 0 \end{cases}$$ ### Part 1: $$f(-4)$$ Since $$-4$$ is less than $$0$$, we use the first part of the piecewise function: $$f(-4) = -4$$ So, $$f(-4) = -4$$. ### Part 2: $$f(0)$$ Since $$0$$ is equal to $$0$$, we use the second part of the piecewise function: $$f(0) = 5(0) + 8 = 0 + 8 = 8$$ So, $$f(0) = 8$$. ### Part 3: $$f(7)$$ Since $$7$$ is greater than $$0$$, we use the second part of the piecewise function: $$f(7) = 5(7) + 8 = 35 + 8 = 43$$ So, $$f(7) = 43$$. ### Summary of Results: - $$f(-4) = -4$$ - $$f(0) = 8$$ - $$f(7) = 43$$ Would you like more details or have any questions? Here are 5 related questions to expand your understanding: 1. How would the function change if the condition for $$x = 0$$ were modified? 2. Can you determine the value of $$f(2)$$ for the given function? 3. What is the domain of the given piecewise function? 4. How would the function behave if the condition were $$x \leq 0$$ instead of $$x < 0$$? 5. What would be the value of $$f(-1)$$? **Tip:** Understanding piecewise functions is key to analyzing how different conditions affect the output based on the input values.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise functions
Formulas
-
Theorems
-
Suitable Grade Level
Grades 10-12