Question

Which of the following is the graph of f(x) = -0.5|x+3| -2?

Answer 1

Answer:

The last graph

Step-by-step explanation:

We transform functions in the following ways:

• multiplying the function by a number to stretch or shrink it
• multiplying by a negative to flip the orientation of the function
• adding/subtracting a value to the input x to shift it horizontally
• adding/subtracting a value to the output (or outside the function operation) to shift it vertically or horizontally.

Looking at the equation we can see $f(x)=-0.5\left|x+3\right|-2$

• Vertically shrunk by 0.5
• Negative leading coefficient to flip the graph's orientation
• Horizontal shift of the vertex of 3 units to the left from (0,-2) to (-3,-2)
• Vertical shift of the vertex of 2 units downward (-3,0) to (-3,-2)

The last graph has vertex (-3,-2) and satisfies the the equation.

Answer 2

Answer: first one

Step-by-step explanation: