Answer:
f(x) has the greatest y-intercept
Step-by-step explanation:
* Lets explain how to solve the problem
- The function f(x) = 7x + 3
- The function g(x) is tangent function with y-intercept at (0 , 2)
- h(x) = 2 sin(3x + π) - 1
* Lets explain how to find the y-intercept
- The y-intercept means the intersection of the graph of the
function with the y- axis
- Any point on the y-axis has x-coordinate = 0, so to find the y-intercept
of any function substitute x in the function by zero
∵ f(x) = 7x + 3
∵ x = 0
∴ f(x) = 3
∴ The y-intercept of f(x) is 3
∵ g(x) has y-intercept at point (0 , 2)
∴ The y-intercept of g(x) is 2
∵ h(x) = 2 sin(3x + π) - 1
∵ x = 0
∴ h(x) = 2 sin(3 × 0 + π) - 1
∴ h(x) = 2 sin(π) - 1
∵ sin(π) = 0
∴ h(x) = 2 (0) - 1 = 0 - 1 = -1
∴ The y-intercept of h(x) is -1
∵ 3 > 2 and 3 > -1
∴ f(x) has the greatest y-intercept
