6'4 Compound Functions

1
6.4 Compound Functions

• A compound function is a combination of
  equations.
• Each problem has two equations, one for a line,
  the other for a parabola.
• Both functions are graphed on the same graph.
• Each function has a condition that dictates what
  values satisfy the equation.
• Each graph will be dotted where the values are
  not valid, and solid where the values are valid.

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Example

• Example
• f(x) -x2 2, x lt 0
• x 2, x ? 0
• Step 1 Find information in order to graph each
  equation.
• 1st equation y -x2 2
• a -1 b 0 c 2
• axis of symmetry x (-b/2a) 0/(2 -1) ? x
  0
• vertex x 0 then y -(0)2 2 ? y 2
  vertex (0, 2)
• 2nd point Let x 1 then y -(1)2 2 ? y 1
  2nd point (1,1)
• 3rd point Use symmetry.

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2nd Equation

• The second equation must be in slope intercept
  form.
• 2nd Equation y x 2
• slope 1/1, y-intercept (0,2)
• Step 2 Use the information calculated to graph
  both equations on the same graph. Use dotted
  lines.

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Conditions

• Step 3 Evaluate the conditions for each graph
  and make that part of the graph solid.
• f(x) -x2 2, x lt 0
• x 2, x ? 0
• For the parabola, the only points valid are those
  where x lt 0.
• Find x 0 on the graph of the parabola and
  darken that part of the parabola.
• For the line, the only points valid are those
  where x ? 0. Find x 0 on the graph of the line
  and darken that part of the line.
• In most cases, these solid parts of the graph
  will meet.
• In this case, the should join at x 0.
• The final part of the graph should be a parabola
  on the left of x 0, and a line on the right of
  x 0.

5
Final Graph

• When making your final graph do not erase the
  dotted segments.
• On the graph below, darken the correct region, as
  shown in class.