Questions: What transformation has been applied to the function in the graph to get the dashed line?
Reflected across the y-axis by adding -1 to the function.
Reflected across the x-axis by adding -1 to the function.
Reflected across the y-axis by multiplying the coefficient of x by -1.
Reflected across the x-axis by multiplying the coefficient of x by -1.
Transcript text: What transformation has been applied to the function in the graph to get the dashed line?
Reflected across the $y$-axis by adding -1 to the function.
Reflected across the $x$-axis by adding -1 to the function.
Reflected across the $y$-axis by multiplying the coefficient of $x$ by -1 .
Reflected across the $x$-axis by multiplying the coefficient of $x$ by -1 .
Solution
Solution Steps
Step 1: Identify the Original Line's Equation
The solid line passes through (0,0) and (4,8). The slope is (8-0)/(4-0) = 2. Since it goes through the origin, its equation is y = 2x.
Step 2: Identify the Transformed Line's Equation
The dashed line passes through (0,0) and (4,-8). Its slope is (-8-0)/(4-0) = -2. Since it goes through the origin, the equation is y = -2x.
Step 3: Determine the Transformation
Comparing y = 2x and y = -2x, we see the coefficient of x has been multiplied by -1. This corresponds to a reflection across the y-axis.
Final Answer
Reflected across the $y$-axis by multiplying the coefficient of $x$ by -1.