Question

Find the equation of the secant line on the given interval for the function f(x) = x^2 - 3 on [-1, 2].

A. y = x - 3
B. y = x - 2
C. y = x^2 - 3
D. y = x + 3

Answer 1

f(2) = 2² - 3 = 4 - 3 = 1

f(-1) = (-1)² - 3 = 1 - 3 = -2

m = (1 - (-2))/(2 - (-1)) = 3/3 = 1

1 = 1(2) + b

1 = 2 + b

b = -1

y = x - 1

None of the choices are correct.

Answer 2

The equation of the secant line on the interval [-1, 2] for the function f(x) = x^2 - 3 is y = x - 1, which corresponds to option B.

Step-by-step explanation:

The equation of the secant line on the interval [-1, 2] for the function f(x) = x^2 - 3 can be found using the slope formula. The slope of the secant line is equal to the difference in the y-values divided by the difference in the x-values. Let's find the slope:

Slope = (f(2) - f(-1)) / (2 - (-1))

Slope = ((2^2 - 3) - ((-1)^2 - 3)) / 3

Slope = (1 - (-2)) / 3

Slope = 3/3

Slope = 1

Now we have the slope of the secant line. To find the equation of the line, we can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line. Let's use the point (2, f(2)):

y - (2^2 - 3) = 1(x - 2)

y - 1 = x - 2

y = x - 1

Therefore, the equation of the secant line is y = x - 1, which corresponds to option B.