About Reflecting Graphs of Functions:
In addition to horizontal and vertical stretches and compressions, we also need to know how to reflect a graph across an axis (x-axis, y-axis). When we reflect a graph across the x-axis, the same x-values will now correspond to the negative of the old y-values. Similarly, when we reflect a graph across the y-axis, the same y-values will now correspond to the negative of the old x-values. Additionally, we will learn how to stretch or shrink a function when a reflection is involved.
Test Objectives
- Demonstrate an understanding of horizontal and vertical stretches and compressions
- Demonstrate the ability to reflect a graph across the x-axis
- Demonstrate the ability to reflect a graph across the y-axis
#1:
Instructions: describe the transformation from f(x) to g(x).
$$a)\hspace{.2em}$$ $$f(x)=\frac{1}{x}$$ $$g(x)=-\frac{3}{x}$$
$$b)\hspace{.2em}$$ $$f(x)=[x]$$ $$g(x)=-3[-x]$$
Watch the Step by Step Video Lesson View the Written Solution
#2:
Instructions: describe the transformation from f(x) to g(x).
$$a)\hspace{.2em}$$ $$f(x)=|x|$$ $$g(x)=-|3x|$$
$$b)\hspace{.2em}$$ $$f(x)=x^2$$ $$g(x)=-\left(\frac{1}{2}\right)^2$$
Watch the Step by Step Video Lesson View the Written Solution
#3:
Instructions: describe the transformation from f(x) to g(x).
$$a)\hspace{.2em}$$ $$f(x)=\frac{1}{x}$$ $$g(x)=-\frac{1}{3x}$$
$$b)\hspace{.2em}$$ $$f(x)=|x|$$ $$g(x)=-\left|\frac{1}{2}x\right|$$
Watch the Step by Step Video Lesson View the Written Solution
#4:
Instructions: describe the transformation from f(x) to g(x).
$$a)\hspace{.2em}$$ $$f(x)=\sqrt{x}$$ $$g(x)=-\frac{1}{2}\sqrt{-x}$$
$$b)\hspace{.2em}$$ $$f(x)=|x|$$ $$g(x)=-|2x|$$
Watch the Step by Step Video Lesson View the Written Solution
#5:
Instructions: describe the transformation from f(x) to g(x).
$$a)\hspace{.2em}$$ $$f(x)=x^3$$ $$g(x)=-(2x)^3$$
$$b)\hspace{.2em}$$ $$f(x)=x^3$$ $$g(x)=-3x^3$$
Watch the Step by Step Video Lesson View the Written Solution
Written Solutions:
#1:
Solutions:
a) vertically stretched by a factor of 3, reflected across the x-axis
b) vertically stretched by a factor of 3, reflected across the x-axis and the y-axis
Watch the Step by Step Video Lesson
#2:
Solutions:
a) horizontally compressed by a factor of 3, reflected across the x-axis
b) horizontally stretched by a factor of 2, reflected across the x-axis
Watch the Step by Step Video Lesson
#3:
Solutions:
a) horizontally compressed by a factor of 3, reflected across the x-axis
b) horizontally stretched by a factor of 2, reflected across the x-axis
Watch the Step by Step Video Lesson
#4:
Solutions:
a) vertically compressed by a factor of 2, reflected across the x-axis and y-axis
b) horizontally compressed by a factor of 2, reflected across the x-axis
Watch the Step by Step Video Lesson
#5:
Solutions:
a) horizontally compressed by a factor of 2, reflected across the x-axis
b) vertically expanded by a factor of 3, reflected across the x-axis
