13. Communicate Precisely A piecewise-defined f is shown. Use function notation to describe the
function and determine the x- and y-intercepts.

  f(x) = {1/2x +3 1/2, for x < 1; -2x +6, for x ≥ 1}

  intercepts: (-7, 0), (3, 0), (0, 3 1/2)

Step-by-step explanation:

function definition

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . line with slope m through point (h, k)

When we solve this for y, we get ...

  y = m(x -h) +k

The slope of a line is the ratio of rise to run. For the left side of the function, the slope is ...

  m = 1/2

For the right side of the function, the slope is ...

  m = -2/1 = -2

The point (1, 4) is common to both parts of the function, so we can write the piecewise function as ...

__

intercepts

Two of the intercepts are shown on the graph. The y-intercept is in the left side of the function, so will be f(0) = 1/2(-1) +4 = 3 1/2.

The x-intercept of the left side of the function is not shown on the graph. We can find it by determining x for f(x) = 0.

  f(x) = 0 = 1/2(x -1) +4

  -4 = 1/2(x -1) . . . add 4

  -8 = x -1 . . . . . multiply by 2

  -7 = x . . . . . . add 1

The x-intercepts are (-7, 0) and (3, 0).

The y-intercept is (0, 3.5).

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

yes

step-by-step explanation:

yes