The new function is g(x) =-1(1/-x) +2.
The transformation of function f(x) to function g(x) is given by g(x)=A f(Bx+ H)+K. where the constant A scales the function vertically. (A negative A reflects the function about the x-axis B scales the function horizontally. (A negative B reflects the function on the y-axis.) H shifts the function horizontally, and K shifts the function vertically.
Convert f(x) to g(x)
where the conversion is g(x)=f(x)+2.
A perpendicular line has negative reciprocal slopes, so for g(x) to be perpendicular to f(x), we need to get the negative reciprocal of -x, which is -1(1/-x)
So, f(x)=-x-2 ; m = -1
From the above information, we get g(x) as follows.
g(x) =-1(1/-x) +2
More problems related to finding new functions for a given function are below.
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Answer:
√2/2
Step-by-step explanation:
If sinP = √2/2,
Rationalize;
√2/2
= √2/2,*√2/√2
√4/2√2
= 2/2√2
= 1/√2
Hence sinP = 1/√2
Take sin inverse of both sies
arcsinP = arcsin1/√2
P = 45 degrees
cos P = Cos 45
= 1/√2
= 1/√2 * √2/√2
= √2/2
Hence the value of cosP is √2/2
Answer as a fraction: 17/6
Answer in decimal form: 2.8333 (approximate)
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Work Shown:
Let's use the two black points to determine the equation of the red f(x) line.
Use the slope formula to get...
m = slope
m = (y2-y1)/(x2-x1)
m = (4-0.5)/(2-(-1))
m = (4-0.5)/(2+1)
m = 3.5/3
m = 35/30
m = (5*7)/(5*6)
m = 7/6
Now use the point slope form
y - y1 = m(x - x1)
y - 0.5 = (7/6)(x - (-1))
y - 0.5 = (7/6)(x + 1)
y - 0.5 = (7/6)x + 7/6
y = (7/6)x + 7/6 + 0.5
y = (7/6)x + 7/6 + 1/2
y = (7/6)x + 7/6 + 3/6
y = (7/6)x + 10/6
y = (7/6)x + 5/3
So,
f(x) = (7/6)x + 5/3
We'll use this later.
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We ultimately want to compute f(g(0))
Let's find g(0) first.
g(0) = 1 since the point (0,1) is on the g(x) graph
We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.
We now use the f(x) function we computed earlier
f(x) = (7/6)x + 5/3
f(1) = (7/6)(1) + 5/3
f(1) = 7/6 + 5/3
f(1) = 7/6 + 10/6
f(1) = 17/6
f(1) = 2.8333 (approximate)
This ultimately means,
f(g(0)) = 17/6 as a fraction
f(g(0)) = 2.8333 as a decimal approximation
Answer:
-7.14
Step-by-step explanation:
Evaluate
−4.2(−2.8 + 4.5)
Open parenthesis
(-4.2 * -2.8) + (-4.2 * 4.5)
= (11.76) + (- 18.9)
= 11.76 - 18.9
= -7.14
NOTE:
Negative (-) × negative (-) = positive (+)
Positive (+) × positive (+) = positive (+)
Negative (-) × positive (+) = negative (-)
Positive (+) × negative (-) = negative (-)
The total amount the Noah receives will be equal to his hourly payment multiplied by the number of working of hours added to the 500$ bonus which he received.
Now, Noah get 28$ per hour and he works for x hours. This means that the payment he gets for working = 28x
Then, we will add the $500 which he received as a bonus.
Doing this, we can get the expression that models his total payment as follows:
y = 28x + 500
