|7x-1|+9

To find the x coordinate of the vertex, set the inside of the absolute value 7x-1 equal to 0. In this case, 7x-1=0.

7x-1=0

Solve the equation 7x-1=0 to find the x coordinate for the absolute value vertex.

Add 1 to both sides of the equation.

7x=1

Divide each term by 7 and simplify.

Divide each term in 7x=1 by 7.

7×7=17

Cancel the common factor of 7.

Cancel the common factor.

7×7=17

Divide x by 1.

x=17

x=17

x=17

x=17

Replace the variable x with 17 in the expression.

y=|7(17)-1|+9

Simplify |7(17)-1|+9.

Simplify each term.

Cancel the common factor of 7.

Cancel the common factor.

y=|7(17)-1|+9

Rewrite the expression.

y=|1-1|+9

y=|1-1|+9

Subtract 1 from 1.

y=|0|+9

The absolute value is the distance between a number and zero. The distance between 0 and 0 is 0.

y=0+9

y=0+9

Add 0 and 9.

y=9

y=9

The absolute value vertex is (17,9).

(17,9)

(17,9)

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(-∞,∞)

Set-Builder Notation:

{x|x∈ℝ}

Substitute the x value -2 into f(x)=|7x-1|+9. In this case, the point is (-2,24).

Replace the variable x with -2 in the expression.

f(-2)=|7(-2)-1|+9

Simplify the result.

Simplify each term.

Multiply 7 by -2.

f(-2)=|-14-1|+9

Subtract 1 from -14.

f(-2)=|-15|+9

The absolute value is the distance between a number and zero. The distance between -15 and 0 is 15.

f(-2)=15+9

f(-2)=15+9

Add 15 and 9.

f(-2)=24

The final answer is 24.

y=24

y=24

y=24

Substitute the x value -1 into f(x)=|7x-1|+9. In this case, the point is (-1,17).

Replace the variable x with -1 in the expression.

f(-1)=|7(-1)-1|+9

Simplify the result.

Simplify each term.

Multiply 7 by -1.

f(-1)=|-7-1|+9

Subtract 1 from -7.

f(-1)=|-8|+9

The absolute value is the distance between a number and zero. The distance between -8 and 0 is 8.

f(-1)=8+9

f(-1)=8+9

Add 8 and 9.

f(-1)=17

The final answer is 17.

y=17

y=17

y=17

Substitute the x value 0 into f(x)=|7x-1|+9. In this case, the point is (0,10).

Replace the variable x with 0 in the expression.

f(0)=|7(0)-1|+9

Simplify the result.

Simplify each term.

Multiply 7 by 0.

f(0)=|0-1|+9

Subtract 1 from 0.

f(0)=|-1|+9

The absolute value is the distance between a number and zero. The distance between -1 and 0 is 1.

f(0)=1+9

f(0)=1+9

Add 1 and 9.

f(0)=10

The final answer is 10.

y=10

y=10

y=10

Substitute the x value 1 into f(x)=|7x-1|+9. In this case, the point is (1,15).

Replace the variable x with 1 in the expression.

f(1)=|7(1)-1|+9

Simplify the result.

Simplify each term.

Multiply 7 by 1.

f(1)=|7-1|+9

Subtract 1 from 7.

f(1)=|6|+9

The absolute value is the distance between a number and zero. The distance between 0 and 6 is 6.

f(1)=6+9

f(1)=6+9

Add 6 and 9.

f(1)=15

The final answer is 15.

y=15

y=15

y=15

The absolute value can be graphed using the points around the vertex (17,9),(-2,24),(-1,17),(0,10),(1,15)

xy-224-117010179115

xy-224-117010179115

Graph |7x-1|+9