Welcome to our tutorial on junior high school functions. Functions are one of the most important concepts in mathematics. Today we will explore key points and clever solution techniques that will help you master function problems with confidence.
Linear functions have the form y equals k x plus b, where k is the slope and b is the y-intercept. The slope tells us how steep the line is, while the y-intercept shows where the line crosses the y-axis. A clever technique is remembering that any two points completely determine a linear function.
Quadratic functions form parabolas. The vertex form y equals a times x minus h squared plus k makes it easy to identify the vertex at point h comma k. The axis of symmetry is the vertical line x equals h. A clever technique is completing the square to convert standard form to vertex form quickly.
Inverse proportional functions have the form y equals k over x, creating hyperbolas with two branches. The key insight is that x times y always equals the constant k. When k is positive, branches appear in quadrants one and three. When k is negative, branches appear in quadrants two and four. The asymptotes are the coordinate axes.
To master function problems, follow these key strategies. First, identify the function type. Then find important points like intercepts and vertices. Use symmetry properties when available. Always check for domain restrictions. Finally, sketch the graph to visualize the solution. With consistent practice of these fundamentals, you'll solve function problems with confidence.