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NISA [10]
3 years ago
12

Given the function f(x) = x^3 + x^2 − 2x + 1, what is the resulting function when f(x) is shifted to the left 1 unit?

Mathematics
1 answer:
Vikki [24]3 years ago
7 0
The resulting function g(x) is ...
  g(x) = f(x +1)
  g(x) = (((x +1) +1)(x +1) -2)(x +1) +1
    = ((x +2)(x +1) -2)(x +1) +1
    = (x² +3x)(x +1) +1
    = x³ +4x² +3x +1

The shifted function g(x) is ...
  g(x) = x³ +4x² +3x +1

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Answer:

y = 30x +50 --- Sam

y = 20x +80 --- Tim

Step-by-step explanation:

Given

Sam                         Tim

х  --- f(x) ---------------  g(x)

1  --- 80   --------------- 100

2  --- 110  --------------- 120

3  --- 140 --------------- 140

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Required

Determine the y value

y value implies the equation of the table

Calculating the equation of Sam

First, we need to take any corresponding values of x and y

(x_1,y_1) = (1,80)

(x_2,y_2) = (4,170)

Next, we calculate the slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{170 - 80}{4 - 1}

m = \frac{90}{3}

m = 30

Next, we calculate the line equation using:

y - y_1=m(x-x_1)

y - 80 = 30(x - 1)

y - 80 = 30x - 30

Make y the subject

y = 30x - 30 + 80

y = 30x +50

Calculating the equation of Tim

First, we need to take any corresponding values of x and y

(x_1,y_1) = (1,100)

(x_2,y_2) = (4,160)

Next, we calculate the slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{160 - 100}{4 - 1}

m = \frac{60}{3}

m = 20

Next, we calculate the line equation using:

y - y_1=m(x-x_1)

y - 100 = 20(x - 1)

y - 100 = 20x - 20

Make y the subject

y = 20x - 20+100

y = 20x +80

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