Transformations of the Graph of f(x) = \sqrt{x}
Apply transformations—shifts, stretches, and reflections—to the graph of f(x) = √x in Grade 9 Algebra. Connect equation parameters to horizontal/vertical changes in the graph.
Key Concepts
Property Vertical translation: The graph of $f(x) = \sqrt{x} + c$ moves up (if $c 0$) or down (if $c<0$). Horizontal translation: The graph of $f(x) = \sqrt{x c}$ moves right (if $c 0$) or left (if $c<0$). Explanation Think of your graph as a video game character. Adding a number outside the root ($+c$) makes it jump up or down. But if the number is inside with $x$ (like $x c$), it's a sneaky side step! Remember, $\sqrt{x c}$ moves right, while $\sqrt{x+c}$ moves left. Examples The graph of $y = \sqrt{x} + 5$ is the parent function shifted 5 units up. The graph of $y = \sqrt{x 4}$ is the parent function shifted 4 units to the right. The graph of $y = \sqrt{x+1}$ is the parent function shifted 1 unit to the left.
Common Questions
What transformations can be applied to f(x) = √x?
You can shift the graph horizontally with f(x) = √(x - h), shift it vertically with f(x) = √x + k, reflect it with f(x) = -√x, or stretch/compress it with f(x) = a√x. These transformations change the graph's position and shape.
How does changing h in f(x) = √(x - h) affect the graph?
Increasing h shifts the starting point to the right, and decreasing h shifts it to the left. The entire graph translates horizontally without changing its shape or vertical position.
How does a negative coefficient outside the radical affect the graph?
A negative coefficient a in f(x) = a√x reflects the graph across the x-axis, flipping it downward. Combined with a magnitude greater than 1, it also stretches the curve away from the x-axis.