Which of the following functions satisfies these two characteristics: f(0) = 0, f(2) = π *
f(x) = -2 sec(x)
f(x) = 7sin(x/4 - 1/29)
f(x) = π cos(πx)
f(x) = 2π cos(x - π/2)

we choose f(x) = π cos(πx)

Step-by-step explanation:

Given the information:

Let analyse all possible answers;

1/ f(x) = -2 sec(x)

when x= 0 we have: f(0) = -2 sec(0) = -2 = -2 wrong

2. f(x) = 7sin(x/4 - 1/29)

when x= 0 we have: f(0) =7sin(0/4 - 1/29) = 7sin(-1/29) = -0.00421 wrong

3. (x) = π cos(πx)

when x= 0 we have: f(0) = πcos(π0) = cos(0) = π0 = 0

when x= 2 we have: f(2) = πcos(π2) = πcos(0) = π

True

4. f(x) = 2π cos(x - π/2)

when x= 0 we have: f(0) = 2π cos(0 - π/2) = 2π cos(-π/2) = 0

when x= 2 we have: f(2) =2π cos(2 - π/2) = 2π0.034 = 0.0697π Wrong

So we choose f(x) = π cos(πx)

the naturalist literary movement was an extension of the realist literary movement, a movement that strove to portray life as it really was hope it

step-by-step explanation:

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b