Test B review, no calculators please help

Question

Answer 1

6) The equation f(x) - g(x) = 0

f(x) = g(x)

The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g are intersect.

From the figure, the linear function f(x) and polynomial function g(x) are intersect at two points.

Therefore, the equation f(x) - g(x) = 0 has two solutions.

Option (b) is correct.

Answer 2

7) The equation y = x² + bx + c

The equation represents in the xy plane a parabola.

Compare it to standard form of parabola y = ax² + bx + c.

a = 1

The equation Passess through (5, 2).

Substitute for (x, y) = (5, 2) in y = x² + bx + c

2 = (5)² + b(5) + c

2 = 25 + 5b + c

2 - 25 = 5b + c

5b + c = - 23 ---> (1)

 

Axis of symmetry x = -b/2a

From the given data x = 3

(- b)/(2a) = 3

Substitute the value of a.

(- b)/[2(1)] = 3

(- b)/2 = 3

- b = 6

b = - 6

Substitute the b value in equation (1).

5(- 6) + c = - 23

- 30 + c = - 23

c = - 23 + 30

c = 7

Substitute b,c in y = x² + bx + c

y = x² - 6x + 7

Solution : c = 7

Option (e) is correct.

Answer 3

8) The rational function h(x) = 2/(x + 3)

We know that all possible values of x is domain of a function.

A rational function is simply fraction and in a fraction the denominator cannot be equal to 0 because it would be undefined.

To find which number make the fraction undefined create an equation where the denominator is not equal to zero.

x + 3 ≠  0

x ≠ - 3

So the domain of the function all real numbers except -3.

Domain set is (- ∞, - 3) U (- 3, ∞).

Option (c) is correct.

Answer 4

9) The functions are f(x) = 4x - x² and g(x) = 2x + 3

f(g(x))

Substitute the expression g(x) = 2x + 3   in the composite function .

= f(2x + 3)

Now substitute expression (2x + 3) in to function f  in the place of x value.

= 4(2x + 3 ) - (2x + 3)²

= 8x + 12 - (4x² + 9 + 12x)

= 8x + 12 - 4x² - 9 - 12x

f(g(x)) = - 4x - 4x² + 3

To find f(g(2)) substitute for x = 2 in f(g(x)).

f(g(2)) = - 4(2) - 4(2)² + 3

= - 8 - 16 + 3

= - 21

f(g(2)) = - 21

Option (d) is correct.