Question

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

Answer 1

QUESTION 1

The given function is

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

If $x$ decreases by $11$, then the new value is $x-11$.

We need to find the value the function at $x-11$ which is

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

This simplifies to

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

The increment in $h(x)$ is given by;

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

This simplifies to,

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

This further simplifies to

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

Therefore the corresponding increment in $h(x)$ is $44$.

QUESTION 2

The given function is

$f(x)=\frac{3}{17}x+2$.

If $x$ increases by $51$, then the new value of $x$ is $x+51$.

The increment in $f(x)$ is given by

$h(x+51)-h(x)=\frac{3}{17}(x+51)+2-(\frac{3}{17}x+2)$

We expand the brackets to get,

$h(x+51)-h(x)=\frac{3}{17}x+9+2-\frac{3}{17}x-2$

We simplify further to obtain,

$h(x+51)-h(x)=9$

Therefore the corresponding increment in $f(x)$ is $9$.

Answer 2

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 $\frac{103}{17}$

Step-by-step explanation:

we are given

f(x)=$\frac{3x+34}{17}$..........(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)=$\frac{3}{17}$(x+51)+2

f(x+51)=$\frac{3x+103+34}{17}$

f(x+51)=$\frac{3x+137}{17}$............(2)

subtracting (1) from (2)

f(x+51)-f(x)=$\frac{3x+137}{17}$- $\frac{3x+34}{17}$

f(x+51)-f(x)=$\frac{103}{17}$

hence it will increase by $\frac{103}{17}$