The function f is defined as follows. f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).

g ( x ) = 4x^2 + 10

Step-by-step explanation:

Solution:-

The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:

Translation guidelines

    Horizontal shifts

  Vertical shifts

   General shift ( Horizontal and Vertical shift )

               f ( x ) - > f ( x ± a ) ± b

We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.

                        f ( x ) = 4x^2 + 6

                        f ( x ) - > f ( x ) + b              

                        g ( x ) = f ( x ) + 4

                        g ( x ) = 4x^2 + 6 + 4

                        g ( x ) = 4x^2 + 10   ... Answer

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

hi there!

the answer to this question is d: 35

step-by-step explanation:

5 to the power of 2 is 25

2 multiplied by 5 is 10

then you add the 2 numbers and you get 35