Test B review, no calculators please help

Question

Answer 1

13) The curve equation y = 2x² + 3x + 1.

Tangent at x = - 2

Using the x - value find the corresponding y - value with the curve.

y = 2(- 2)² + 3( - 2) + 1

y = 8 - 6 + 1

y = 3

Tangent point is ( -2 , 3).

 

y = 2x² + 3x + 1

Differentiating on each side with respect to x.

y' = 4x + 3

Substitute x = - 2 in above equation.

y' = 4(- 2) + 3

y' = - 8 + 3

y' = - 5

This is the slope(m) of the tangent line at (- 2, 3).

 

To find the tangent line equation, substitute the values of m = - 5 and (x, y) = (- 2, 3)  in the slope intercept form of an equation y = mx + b.

3 = - 5(- 2) + b

3 = 10 + b

b = - 7

Substitute m = - 5 and b = - 7 in y = mx + b.

y = - 5x - 7

Equation of tangent line is y = - 5x - 7.

Option (a) is correct.

Answer 2

14) The rational function f(x) = (x² - 7x + 12)/(x - 3)

Write the above rational function in lowest terms.

Factorize the numerator of rational function.

x² - 7x + 12

= x² - 4x - 3x + 12

= x(x - 4)- 3(x - 4)

= (x - 4)(x - 3)

Now the function f(x) = [(x - 4)(x - 3)]/(x - 3)

f(x) = x - 4

Change f(x) to y.

y = x - 4

Zeros of the function is where the graph crosses the x axis(x intercepts).

To find x intercept substitute y = 0 in y = x - 4.

0 = x - 4

x = 4

Zeros of the f(x) = (x² - 7x + 12)/(x - 3) is only 4.

Option (d) is correct.

Answer 3

15) The line 8y - 3x = 24

Write the above equation slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

8y = 3x + 24

y = (3/8)x + (24/8)

y = (3/8)x + 3

Slope m = 3/8 and y intercept is 3.

 

Find the x intercept, by substituting y = 0 in y = (3/8)x + 3.

0 = (3/8)x + 3

(3/8)x = - 3

x = - 3(8/3)

x = - 8

x intercept is - 8.
Option (d) is correct.