Each function is defined by two equations. The equation in...

Each function is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for nonnegative numbers in the domain. Find the indicated function values. $f(x)=\left\{\begin{array}{ll}6 x-1 & \text { if } x<0 \\ 7 x+3 & \text { if } x \geq 0\end{array}\right.$ a. $f(-3)$ b. $f(0)$ c. $f(4)$ d. $f(-100)+f(100)$

Each function is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for nonnegative numbers in the domain. Find the indicated function values.
$f(x)=\left\{\begin{array}{ll}6 x-1 & \text { if } x<0 \\ 7 x+3 & \text { if } x \geq 0\end{array}\right.$
a. $f(-3)$
b. $f(0)$
c. $f(4)$
d. $f(-100)+f(100)$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Linear Functions

Linear functions, typically expressed in the form f(x) = ax + b, represent straight-line relationships between the input and output. They are often used in piecewise functions due to their simplicity and ease of calculation.

Function Evaluation

Function evaluation is the process of substituting a specific value into the function's expression and calculating the output. For piecewise functions, this involves first determining which condition the value satisfies before performing the substitution.

Conditional Definitions

Conditional definitions refer to specifying different expressions for a function based on conditions related to the input value. This is essential when a function's rule changes depending on the domain subset the input belongs to.

Domain Partitioning

Domain partitioning involves dividing the set of all possible inputs into disjoint intervals or cases, each with its own rule in a piecewise function. This helps ensure that the function is well-defined over its entire domain.

Piecewise Functions

Piecewise functions are defined by different expressions over different parts of the domain. This allows one function to behave differently in different intervals, such as for negative versus nonnegative inputs.

Transcript

Please give Ace some feedback