Final answer:
The x-intercepts and y-intercepts of the given functions are explained step-by-step.
Step-by-step explanation:
1) The x-intercept of a function occurs when the value of y is 0. To find the x-intercept, set f(x) equal to 0 and solve for x:
x + 7 = 0
x = -7
Therefore, the x-intercept is -7.
The y-intercept occurs when the value of x is 0. To find the y-intercept, plug in x = 0 into the function:
f(0) = 0 + 7 = 7
Therefore, the y-intercept is 7.
2) To find the x-intercepts of g(x), set g(x) equal to 0 and solve for x:
4 - x^2 = 0
x^2 = 4
x = ±2
Therefore, the x-intercepts are -2 and 2.
The y-intercept can be found by plugging in x = 0 into the function:
g(0) = 4 - 0^2 = 4
Therefore, the y-intercept is 4.
3) To find the x-intercept of h(x), set h(x) equal to 0 and solve for x:
√(x - 5) - 3 = 0
√(x - 5) = 3
x - 5 = 9
x = 14
Therefore, the x-intercept is 14.
The y-intercept can be found by plugging in x = 0 into the function:
h(0) = √(0 - 5) - 3 = -3
Therefore, the y-intercept is -3.