Math  /  Algebra

QuestionEspañol
Suppose that the function gg is defir g(x)={3 if x<10 if x=11 if x>1g(x)=\left\{\begin{array}{cl} -3 & \text { if } x<-1 \\ 0 & \text { if } x=-1 \\ 1 & \text { if } x>-1 \end{array}\right.
Graph the function gg.

Studdy Solution

STEP 1

1. The function g(x) g(x) is defined piecewise, meaning it has different expressions based on the value of x x .
2. The graph of a piecewise function is constructed by graphing each piece over its specified interval.
3. The function has three distinct pieces to graph.

STEP 2

1. Identify the pieces of the piecewise function.
2. Graph each piece on the coordinate plane.
3. Combine the pieces to form the complete graph of the function.

STEP 3

Identify the pieces of the piecewise function g(x) g(x) :
- g(x)=3 g(x) = -3 for x<1 x < -1 - g(x)=0 g(x) = 0 for x=1 x = -1 - g(x)=1 g(x) = 1 for x>1 x > -1

STEP 4

Graph the first piece g(x)=3 g(x) = -3 for x<1 x < -1 :
- This is a horizontal line at y=3 y = -3 for all x x values less than 1-1. - The line will approach but not include the point (1,3)(-1, -3), so use an open circle at (1,3)(-1, -3).

STEP 5

Graph the second piece g(x)=0 g(x) = 0 for x=1 x = -1 :
- This is a single point at (1,0)(-1, 0). - Use a solid dot to indicate that the function value at x=1 x = -1 is exactly 0 0 .

STEP 6

Graph the third piece g(x)=1 g(x) = 1 for x>1 x > -1 :
- This is a horizontal line at y=1 y = 1 for all x x values greater than 1-1. - The line will start immediately after (1,1)(-1, 1), so use an open circle at (1,1)(-1, 1).

STEP 7

Combine the pieces to form the complete graph of the function:
- The graph consists of three parts: a horizontal line at y=3 y = -3 for x<1 x < -1 , a point at (1,0)(-1, 0), and a horizontal line at y=1 y = 1 for x>1 x > -1 . - Ensure the open and closed circles are correctly placed to indicate the function's behavior at x=1 x = -1 .
The graph of the function g(x) g(x) is now complete.

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