Question

Help please

For each comparison below, select the correct symbol (<,>, or =) that indicates the relationship between the first and second quantity.

Answer 1

Explanation:

What grade are you in bc I did this

Answer 2

• See below

Explanation:

f(x) is quadratic function and g(x) is linear (since AP in the right column).

Find the equation of the function f(x), use the points on the graph:

• f(x) = ax² + bx + c

• c = 5 as the y-intercept is (0, 5)
• a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
• a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4

The function is:

• f(x) = -x² + 4x + 5

Find the equation of g(x)

Find the slope of g(x):

• m = (1 - 7)/(-1 + 4) = -2

Use (-4, 7) to find its equation:

• y - 7 = -2(x + 4)
• y = -2x + 7 - 8
• y = -2x - 1

See the required comparison below

The y-intercepts:

• f(x) ⇒ 5,
• g(x) ⇒ -1
• -5 < - 1

Values at x = 3:

• f(3) = -3² + 4(3) + 5 = 8
• g(3) = -2(3) - 1 = - 7
• 8 > 7

Average rate of change in the interval [2,5]:

• f(x) ⇒ (0 - 9)/(5 - 2) = -3
• g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
• -3 < -2

Max of function in the interval [-5, 5];

• f(x) ⇒ 9, vertex of the function
• g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
• 9 = 9