📘 functions

1. **State the problem:** We have two functions $f$ and $g$ with given domains and ranges.

1. The problem asks: Which graph represents a function? 2. Recall the definition of a function: For each input $x$, there must be exactly one output $y$.

1. **Problem e)**: Given the domain $\{-2,0,2,3\}$ and range $\{-4,2,1,12,3,4\}$, determine if these sets can represent a function. 2. **Explanation**: A function assigns exactly o

1. **Problem statement:** Find the domain and range of the composition $g \circ f$, where $f$ and $g$ are functions with given domains and ranges.

1. **State the problem:** Laurie's function $f$ takes a word as input and outputs the number of letters in that word.

1. **State the problem:** Find the domain and range of the composition of two functions $g \circ f$, where $f$ and $g$ have given domains and ranges.

1. The problem describes a mapping from the set \{8,7,0\} to the set \{4,-1,-3\} with the pairs (8 \to 4), (7 \to -1), and (0 \to -3). 2. This is a function where each input from t

1. **State the problem:** We need to estimate the value of $k(j(2))$ using the given graphs of $j(x)$ and $k(x)$ for $-1 \leq x \leq 5$. 2. **Find $j(2)$ from the graph of $j(x)$:*

1. **State the problem:** We are given functions \(g(x) = x^4\), \(h(x) = 3^x\), and \(f(x) = 7 + 3x\). We need to find the value of \(k\) such that \(h(3x) = k^x\). 2. **Write the

1. The problem asks which graph represents a function that is periodic and sinusoidal. 2. A periodic function repeats its values in regular intervals or periods.

1. Problem: Determine which of the following figures represent the curve of a function in which its range $\neq$ its domain. 2. Definitions and rules: The domain is the set of x-va

1. The problem asks which figure represents a function where the range is not equal to the domain. 2. Let's analyze each figure:

1. Locate and label the points and identify their quadrants: - Point (-1, -3) is in Quadrant III (both x and y negative).

1. **Stating the problem:** We are given a piecewise function: