Answer:
The true statement is answer A
The y-intercept of g(x) is less than the y-intercept of f(x)
Step-by-step explanation:
* Lets explain the meaning of x-intercept and y-intercept
# x-intercept means the line cross the x-axis at which point
∵ Any point lies on the x-axis has x-coordinate but its y-coordinate
is zero
∴ To find the x- intercept in any function you must to chose the
value of x when y = 0
* Similar
# y-intercept means the line cross the y-axis at which point
∵ Any point lies on the y-axis has y-coordinate but its x-coordinate
is zero
∴ To find the y- intercept in any function you must to chose the
value of y when x = 0
* Now lets solve the problem
- Find the x-intercept and the y- intercept for f(x) and g(x)
# In f(x)
- From the table there is a point (0 , -4)
∵ x = 0
∴ The y-intercept of f(x) = -4
- From the table there is a point (16 , 0)
∵ y = 0
∴ The x-intercept of f(x) = 16
# In g(x)
- From the equation g(x) = 4√x - 8
- To find the y-intercept put x = 0
∵ g(x) = 4√x - 8 and x = 0
∴ g(x) = 4√0 - 8 = -8
∴ The y-intercept of g(x) = -8
- To find the x-intercept put y = 0
∵ g(x) = 4√x - 8 and y = 0 ⇒ g(x) = 0
∴ 0 = 4√x - 8 ⇒ add 8 for both sides
∴ 8 = 4√x ⇒ divide both sides by 4
∴ 2 = √x ⇒ square the two sides
∴ (2)² = (√x)²
∴ 4 = x
∴ The x-intercept of g(x) = 4
- From the answers above
∵ y-intercept of f(x) = -4
∵ y-intercept of g(x) = -8
∵ -8 is less than -4
∴ The y-intercept of g(x) is less than the y-intercept of f(x)
* The true statement is answer A
