First calculate the change in y over the change in x:
by - ay -1 - 1 -2
———— = ——— = —— = 1
bx - ax -2 - 0 -2
The slope is 1:
Second set up the equation in y = mx + b form (m is your slope!) ...
y = (1)x + b
... and plug in either point you have used (A or B)
A(0,1)
1 = (1)(0) + b
1 = b
Now you have your equation: y = 1x + 1
Your final step is to plug in point C to solve for your missing variable:
y = (1)(5) + 1
y = 6
the value of H therefore is 6
First, we want to solve for b.
In order to solve for b, we plug in x=6 and f(x)=7 into the equation, since we know f(6)=7
7 = (3/2)(6) + b
7 = 9 + b
Subtract both sides by 9
b = -2
Now, let's insert this value into the equation
f(x) = (3/2)x - 2
Now, plug in x = -2 into the equation to calculate f(-2)
f(-2) = (3/2)(-2) - 2
= -3 -2
= -5
Thus, your answer is A.
Have an awesome day! :)
Recall that √x has a domain of x ≥ 0.
So, f(x) is defined as long as
(x + 1)/(x - 1) ≥ 0
• We have equality when x = -1
• Otherwise (x + 1)/(x - 1) is positive if both x + 1 and x - 1 are positive, or both are negative:


Then the domain of f(x) is
x > 1 or x ≤ -1
On the other hand, g(x) is defined by two individual square root expressions with respective domains of
• x + 1 ≥ 0 ⇒ x ≥ -1
• x - 1 ≥ 0 ⇒ x ≥ 1
but note that g(1) is undefined, so we omit it from the second domain.
Then g(x) is defined so long as both x ≥ -1 *and* x > 1 are satisfied, which means its domain is
x > 1
f(x) and g(x) have different domains, so they are not the same function.
Answer:
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Explanation: