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A function h is defined by h(x)=−4x−72. If x decreases by 11, by how much does h(x) increase?

A function f is defined by f(x)= 3/17 x+2. If x increases by 51, by how much does f(x) increase?

Respuesta :

kudzordzifrancis

QUESTION 1

The given function is


[tex]h(x)=-4x-72[/tex]

If [tex]x[/tex] decreases by [tex]11[/tex], then the new value is [tex]x-11[/tex].


We need to find the value the function at [tex]x-11[/tex] which is


[tex]h(x-11)=-4(x-11)-72[/tex]


This simplifies to


[tex]h(x-11)=-4x+44-72[/tex]


The increment in [tex]h(x)[/tex] is given by;


[tex]h(x-11)-h(x)=-4x+44-72-(-4x-72)[/tex]


This simplifies to,

[tex]h(x-11)-h(x)=-4x+44-72+4x+72[/tex]


This further simplifies to


[tex]h(x-11)-h(x)=44[/tex]


Therefore the corresponding increment in [tex]h(x)[/tex] is [tex]44[/tex].


QUESTION 2

The given function is

[tex]f(x)=\frac{3}{17}x+2[/tex].


If [tex]x[/tex] increases by [tex]51[/tex], then the new value of [tex]x[/tex] is [tex]x+51[/tex].


The increment in [tex]f(x)[/tex] is given by

[tex]h(x+51)-h(x)=\frac{3}{17}(x+51)+2-(\frac{3}{17}x+2)[/tex]


We expand the brackets to get,


[tex]h(x+51)-h(x)=\frac{3}{17}x+9+2-\frac{3}{17}x-2[/tex]


We simplify further to obtain,


[tex]h(x+51)-h(x)=9[/tex]


Therefore the corresponding increment in [tex]f(x)[/tex] is [tex]9[/tex].





bc160402048

Answer#1

increase by 44

Step-by-step explanation:

Given function is

h(x)=-4x-72........(1)

we have tofind

h(x-11)=?

replace x by x-11 in (1) we get

h(x-11)=-4(x-11)-72

h(x-11)=-4x+44-72

h(x-11)= -4x-28...........(2)

and h(x)= -4x-72

subtracting (1) from (2)

we get

h(x-11)- h(x)= -4x-28 - (-4x-72)

h(x-11)- h(x)= -4x-28 +4x+72

h(x-11)- h(x)= 44

hence it increases by 44

Answer#2

it will increase by [tex]\frac{103}{17}[/tex]

Step-by-step explanation:

we are given

f(x)=[tex]\frac{3x+34}{17}[/tex]..........(1)

we have to find

f(x+51)=?

and then (x+51)-f(x)=?

for f(x+51) we will replace x by x+51 in (1)

f(x+51)=[tex]\frac{3}{17}[/tex](x+51)+2

f(x+51)=[tex]\frac{3x+103+34}{17}[/tex]

f(x+51)=[tex]\frac{3x+137}{17}[/tex]............(2)

subtracting (1) from (2)

f(x+51)-f(x)=[tex]\frac{3x+137}{17}[/tex]- [tex]\frac{3x+34}{17}[/tex]

f(x+51)-f(x)=[tex]\frac{103}{17}[/tex]

hence it will increase by [tex]\frac{103}{17}[/tex]