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benwill0702
15.07.2019 •
Mathematics
Translate this sentence into an equation.
the difference of mai's age and 12 is 60
Solved
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Ответ:
72
Step-by-step explanation:
Ответ:
60-12= A
Ответ:
Part A) shift left 2 units or shift up 10 units
Part B) k=-2 and k=10
Part C) g(x)=f(x+2) or g(x)=f(x)+10
Step-by-step explanation:
Find the equation of f(x)
we have the points(0,-2) and (1,3)
The slope m is
The equation in slope intercept form is
we have
substitute
Find the equation of g(x)
we have the points(0,8) and (-1,3)
The slope m is
The equation in slope intercept form is
we have
substitute
Part A and part B: Describe two types of transformations that can be used to transform f(x) to g(x). Solve for k in each type of transformation
First type of transformation
we have
Find the x-intercepts of f(x) and g(x) (values of x when the value of the function is equal to zero)
For f(x)=0
For g(x)=0
f(x) > g(x)
The translation of the x-intercept is
(0.4,0) > (-1.6,0)
so
The rule of the translation is
(x,y) > (x+k,y)
(0.4,0) > (0.4+k,0)
so
(0.4+k,0)=(-1.6,0)
Solve for k
0.4+k=-1.6 > k=-1.6-0.4=-2.0
therefore
The rule of the translation is
(x,y) > (x-2,y)
That means > The translation is 2 units at left
Second type of transformation
we have
The y-intercepts (values of the function when the value of x is equal to zero)
f(x) > (0,-2)
g(x) > (0,8)
The translation of the y-intercept is
f(x) >g(x)
(0,-2) > (0,8)
so
The rule of the translation is
(x,y) > (x,y+k)
(0,-2) > (0,-2+k)
so
(0,-2+k)=(0,8)
Solve for k
-2+k=8 > k=8+2=10
therefore
The rule of the translation is
(x,y) > (x,y+10)
That means > The translation is 10 units up
Part C) Write an equation for each type of transformation that can be used to transform f(x) to g(x).
First transformation
The rule of the translation is
(x,y) > (x-2,y)
f(x) > g(x)
so
so
therefore
> is ok
Second transformation
The rule of the translation is
(x,y) > (x,y+10)
f(x) > g(x)
so
so
therefore
> is ok