Reflections of the Graph of f(x) = \sqrt{x}
Reflect the graph of f(x) = √x across the x- or y-axis in Grade 9 Algebra. Understand how multiplying by -1 inside or outside the function flips the graph.
Key Concepts
Property If $f(x) = \sqrt{x}$, then $g(x) = \sqrt{x}$ is a reflection across the x axis. If $f(x) = \sqrt{x}$, then $g(x) = \sqrt{ x}$ is a reflection across the y axis. Explanation Imagine the x and y axes are mirrors! A negative sign outside the root ($ \sqrt{x}$) flips the graph downwards over the horizontal x axis mirror. A negative sign inside the root ($\sqrt{ x}$) flips the graph sideways over the vertical y axis mirror, creating a backward swooping curve. It’s all about where you place that negative! Examples The graph of $y = \sqrt{x}$ is the parent function flipped upside down across the x axis. The graph of $y = \sqrt{ x}$ is the parent function flipped backward across the y axis. The graph of $y = \sqrt{x} 2$ is flipped across the x axis and then shifted 2 units down.
Common Questions
What is Reflections of the Graph of f(x) = \sqrt{x} in Grade 9 Algebra?
Property If , then is a reflection across the x-axis Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Reflections of the Graph of f(x) = \sqrt{x} problems step by step?
A negative sign outside the root () flips the graph downwards over the horizontal x-axis mirror Use this method consistently to avoid common errors.
What is a common mistake when studying Reflections of the Graph of f(x) = \sqrt{x}?
A negative sign inside the root () flips the graph sideways over the vertical y-axis mirror, creating a backward-swooping curve Always check your work by substituting back into the original problem.