Test your knowledge: Evaluate functions from visual data

📚 Quick Study Guide

• 📊 Understanding Functions: A function relates an input to an output. Visually, this is often represented as a graph where each input (x-value) has only one output (y-value).
• 📈 Vertical Line Test: A graph represents a function if and only if every vertical line intersects the graph at most once.
• 🔍 Reading Graphs: To evaluate a function $f(x)$ at a specific value $x = a$, find the point on the graph where the x-coordinate is $a$. The y-coordinate of that point is $f(a)$.
• 📝 Domain and Range: The domain is the set of all possible input values (x-values), and the range is the set of all possible output values (y-values).
• 💡 Intercepts: The x-intercept is where the graph crosses the x-axis (y=0), and the y-intercept is where the graph crosses the y-axis (x=0).
• 🧮 Slope: The slope of a linear function represents the rate of change (rise over run).
• 📐 Transformations: Understanding how basic functions are shifted, stretched, or reflected helps in quickly evaluating more complex functions.

Practice Quiz

1. Question 1: Which of the following graphs represents a function?
   1. A) A circle
   2. B) A parabola opening to the right
   3. C) A straight line with a positive slope
   4. D) A vertical line
2. Question 2: Given a graph of a function $f(x)$, if the point (3, 5) lies on the graph, what is the value of $f(3)$?
   1. A) 3
   2. B) 5
   3. C) 8
   4. D) It cannot be determined.
3. Question 3: The graph of a function $g(x)$ intersects the x-axis at x = -2. What is the value of $g(-2)$?
   1. A) -2
   2. B) 0
   3. C) 2
   4. D) It cannot be determined.
4. Question 4: Which of the following transformations of a function $h(x)$ would shift the graph upwards by 3 units?
   1. A) $h(x + 3)$
   2. B) $h(x - 3)$
   3. C) $h(x) + 3$
   4. D) $h(x) - 3$
5. Question 5: A linear function passes through the points (0, 2) and (1, 5). What is the y-intercept of this function?
   1. A) 0
   2. B) 2
   3. C) 3
   4. D) 5
6. Question 6: The domain of a function is represented by which axis on the graph?
   1. A) y-axis
   2. B) x-axis
   3. C) z-axis
   4. D) Both x and y axis
7. Question 7: If a graph is symmetric with respect to the y-axis, which of the following is true?
   1. A) $f(x) = f(-x)$
   2. B) $f(x) = -f(x)$
   3. C) $f(x) = f(x+1)$
   4. D) $f(x) = -f(-x)$