Quizzes > High School Quizzes > Mathematics
Unit 2 Functions Practice Test
Ace your quiz with a detailed answer key
Study Outcomes
- Identify and interpret function notation accurately.
- Analyze graphs of functions to determine key characteristics.
- Apply function transformations to modify and sketch graphs.
- Evaluate how changes in function expressions affect their graphical representation.
- Synthesize information from notation and graphs to solve problem-based function questions.
Unit 2 Understanding Functions Answer Key Cheat Sheet
- Function Notation - Think of f(x) as a magic machine: you feed it x and it spits out a result. For example, if f(x)=x², then f(3)=9 - simple as that! Grasping this notation unlocks all sorts of function wizardry. Transformations of Functions - MathBitsNotebook(A2)
- Graphing Functions - Plotting a function is like connecting the dots on a treasure map: substitute x values, find the points, and draw a smooth curve. For instance, with f(x)=x² you'd mark (0,0), (1,1), and (-1,1). A clear graph reveals hidden behavior at a glance! Transformations of Functions - MathBitsNotebook(A2)
- Vertical Shifts - Adding or subtracting a constant k to f(x) moves your curve up or down like sliding it on a ruler. So f(x)+3 nudges everything 3 units skyward, while f(x)−2 drops it down. Mastering this helps you predict how graphs change. Transformations of Functions - MathBitsNotebook(A2)
- Horizontal Shifts - Replace x with (x−h) to move the graph h units right, or with (x+h) to shift it left. For example, f(x−2) scoots the entire curve 2 steps right on the x-axis. It's like panning the camera left or right! Transformations of Functions - MathBitsNotebook(A2)
- Reflections - Multiply f(x) by −1 to flip the graph over the x-axis, turning peaks into valleys. Swap x for −x to mirror over the y-axis, flipping it sideways. It's a fun way to see how functions behave when mirrored! Transformations of Functions - MathBitsNotebook(A2)
- Vertical Stretches & Compressions - Multiply f(x) by a factor a>1 to stretch the graph tall or by 0Transformations of Functions - MathBitsNotebook(A2)
- Horizontal Stretches & Compressions - Change x to (x/b) to stretch the graph wide if b>1 or compress it if 0Transformations of Functions - MathBitsNotebook(A2)
- Combining Transformations - Stack transformations like a sandwich: f(x−2)+3 shifts right 2 units then up 3 units in one go. The order matters - like mixing colors, you'll get different results. Practice layering moves to ace complex graphs! Practice: Combining Function Transformations - MathBitsNotebook(A1)
- Identifying Transformations - Given g(x)=−2(x+1)²+4, pinpoint the flip, stretch, and shifts: reflection, vertical stretch, left shift, and upward move. Spotting each change makes graphing quick and intuitive. Test yourself with real examples! Practice Identifying Function Transformations - MathBitsNotebook(A1)
- Online Practice Resources - Dive into interactive lessons, video tutorials, and quizzes to reinforce everything you've learned about function transformations. Consistent practice builds confidence and speed. Level up your skills with top-quality resources! Transformations Explained: Definition, Examples, Practice & Video Lessons