Given that (9,-8) is on the graph of f(x), find the corresponding point for the function f(3/4x)

The corresponding point for the function f(3/4 x) is (12 , -8)

Step-by-step explanation:

* Lets revise the horizontal stretch or compress

- A horizontal stretching is the stretching of the graph away from

 the y-axis

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

# if k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally

 compressed by dividing each of its x-coordinates by k.

# if 0 < k < 1 (a fraction), the graph y = f(k·x) is the graph of f(x)

  horizontally stretched by dividing each of its x-coordinates by k.

* Now lets solve the problem

- The function f(x) will be the function f(3/4 x)

∵ The x multiplied by a constant

∴ f(x) stretched or compressed horizontally

∵ f(x) ⇒ f(k · x)

∵ f(x) ⇒ f(3/4 x)

∴ k = 3/4 ⇒ less than 1

∵ 0 < k < 1

∴ f(x) starched horizontally

∴ Divide each of its x-coordinates by k

∵ k = 3/4

∴ Divide each of its x-coordinates by 3/4

∵ Point (9 , -8) is on the graph of f(x)

- Find the corresponding point on the graph f(3/4 x) by dividing

 x-coordinate by 3/4

∵ x = 9

∴ The corresponding x = 9 ÷ 3/4 = 9 × 4/3 = 36/3 = 12

∴ The corresponding point is (12 , -8)

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

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