REFLECTING GRAPHS AND SYMMETRY

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Presentation transcript:

REFLECTING GRAPHS AND SYMMETRY Section 4.3

x-axis y-axis Line y = x Absolute value of a graph Around a point REFLECTING GRAPHS x-axis y-axis Line y = x Absolute value of a graph Around a point

GRAPH USING CALCULATOR How are the graphs of y=f(x) and y = - f(x) related? Reflected over the x-axis!!

Any negative y values are reflected GRAPH Any negative y values are reflected over the x-axis!!

GRAPH USING CALCULATOR How are the graphs of y = f(x) and y = f(-x) related? Reflected over the y-axis!!

GRAPH The graph is reflected over the line y = x!! How is the graph of an equation affected when you interchange the variables in the equation? The graph is reflected over the line y = x!!

Sketch the graphs of:

Sketch the graphs of:

Sketch the graph and the reflection in the line y = x Sketch the graph and the reflection in the line y = x. Also, give the equation of the reflected graph.

Bellwork Given an isosceles right triangle shown below. Express the Area, A, of the triangle as a function of the hypotenuse, c. c a

Summary of Symmetry X-axis y = -f(x) (make y negative) Y-axis y = f(-x) (make x negative) Line y = x x = f(y) (switch x and y) Origin y = -f(-x) (both x and y are negative)

Is there any symmetry in the graph of the functions?

Use symmetry to sketch the graph of

Use symmetry to sketch the graph of

Cubic Functions and Symmetry: What type of symmetry is in a cubic? What is the point of symmetry?

Given the polynomial below, what is the point of symmetry?

The graph of a cubic function has a local max at (-5, 6) and a point of symmetry a (-1, 2). What is the local minimum?