Question

Obtaining Information about the Graph of a function 1. Consider the function f(x)=x+1/ x+2 a) is the point (1,1/2 ) on the graph of ?? b) If x=2, what in f(x) ? What point is on the graph of 1? c) If f(x)=2, what is x ? What point is on the graph of t ? d) What are the x-intercepts of the graph? What points are on the graph? e) What is the y-intercept of the graph? What point is on the graph?

Answer 1

a) To determine if the point (1, 1/2) is on the graph of the function f(x) = x+1 / x+2, we can substitute x = 1 into the function to check if we get y = 1/2.

f(1) = (1+1) / (1+2) = 2/3

Since f(1) is not equal to 1/2, the point (1, 1/2) is not on the graph of the function f(x) = x+1 / x+2.

b) To find f(2), we can substitute x = 2 into the function.

f(2) = (2+1) / (2+2) = 3/4

So, if x = 2, the point on the graph of f(x) would be (2, 3/4).

c) To find the value of x when f(x) = 2, we can set the function equal to 2 and solve for x.

2 = x+1 / x+2

Multiplying both sides by x+2 gives:

2x + 4 = x + 1

Simplifying gives:

x = -3

So, if f(x) = 2, the point on the graph of f(x) would be (-3, 2).

d) To find the x-intercepts of the graph, we can set y equal to zero and solve for x.

0 = x+1 / x+2

Multiplying both sides by x+2 gives:

0 = x + 1

Simplifying gives:

x = -1

So, the x-intercept of the graph is (-1, 0).

e) To find the y-intercept of the graph, we can set x equal to zero and evaluate the function.

f(0) = (0+1) / (0+2) = 1/2

So, the y-intercept of the graph is (0, 1/2).

Explanation: