Question

Which function is shown in the graph?

y = | x | + 4

y = | x + 4 |

y = | x | -­ 4

y = | x ­- 4 |

Answer 1

`y=|x-4|`

Explanation:

`"consider the intercepts, that is where it crosses the"`
`"x and y axes"`

`•" let x = 0, for y-intercept"`

`• " let y = 0 for x-intercept"`

`x=0toy=|-4|=4larrcolor(red)"y-intercept"`

`y=0to|x-4|=0`

`rarrx-4=0rArrx=4larrcolor(red)"vertex"`

Answer 2

See a solution process below:

Explanation:

First, we can eliminate some functions by evaluating them for `x = 0`, which, according to the graph should give a result of `4`

• Equation 1: `y = abs(0) + 4 = 4` Still a possibility

• Equation 2: `y = abs(0 + 4) = 4` Still a possibility

• Equation 3: `y = abs(0) - 4 = -4` Rule this one out.

• Equation 4: `y = abs(0 - 4) = abs(-4) = 4` Still a possibility

Next, we can evaluate the three remaining functions for `x = 4` which should give a result of `0`

• Equation 1: `y = abs(4) + 4 = 8` Rule this one out.

• Equation 2: `y = abs(4 + 4) = 8` Rule this one out.

• Equation 4: `y = abs(4 - 4) = abs(0) = 0` This is the one!

If we had selected `x = 4` first we would of still had to try another value. Equation 3 would of evaluated as:

• Equation 3: `y = abs(4) - 4 = 0` This would of still been a possibility