Find the x- and y-intercepts of the function f(x) = log(2x + 1) − 1.
1 answer:
Answer:
The y-intercept is -1
The x-intercept is 4.5
Step-by-step explanation:
We have the following equation:
f(x) = log(2x+1) - 1
The y intercept is the value of f(x) when x is equal to 0, so replacing x by 0 and solving for f(x), we get:
f(0) = log(2*0 + 1 ) -1
f(0) = log(1) - 1
f(0) = 0 - 1 = -1
Additionally, the x-intercept is the value of x when f(x) is equal to 0. So, replacing f(x) by 0 and solving for x, we get:
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2 2/3 - 3/5
First, we can start by changing 2 2/3 to an improper fraction. To do this, we can use the rule: a b/c = ac+b/c. All we need to do is insert our numbers into the form of the rule.
Second, we can now start simplifying. (2 × 3 = 6 and 6 + 2 = 8).
Third, now we have change our denominators to be the same. To do this, we can start out by finding the least common denominator (LCD). List the multiples of both of the current denominators (3 and 5) and find the first common one.
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
Since 15 is our first common multiple, it is now our LCD.
Fourth, now we can multiply to change our denominators. Using our current denominators, we have to multiply by let's say (x / a variable). Basically, what can you multiply by 3 to get 15? That would be (3 × 5 = 15). For our other fraction, what would we multiply by 5 to get 15? (5 × 3 = 15). Remember, whatever you do to the bottom you must do to the top.
Fifth, we can now combine our denominators, which will make us have to add both of the numerators together.
Sixth, our last step is to convert the fraction into a mixed fraction. How you do this is to divide the numerator by the denominator. We would set up something like this: 31 ÷ 15 = 2.066667. That decimal in fraction form is 2 1/15, which is our answer.
Answer in fraction form:
Answer in decimal form:
First, we can start by changing 2 2/3 to an improper fraction. To do this, we can use the rule: a b/c = ac+b/c. All we need to do is insert our numbers into the form of the rule.
Second, we can now start simplifying. (2 × 3 = 6 and 6 + 2 = 8).
Third, now we have change our denominators to be the same. To do this, we can start out by finding the least common denominator (LCD). List the multiples of both of the current denominators (3 and 5) and find the first common one.
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
Since 15 is our first common multiple, it is now our LCD.
Fourth, now we can multiply to change our denominators. Using our current denominators, we have to multiply by let's say (x / a variable). Basically, what can you multiply by 3 to get 15? That would be (3 × 5 = 15). For our other fraction, what would we multiply by 5 to get 15? (5 × 3 = 15). Remember, whatever you do to the bottom you must do to the top.
Fifth, we can now combine our denominators, which will make us have to add both of the numerators together.
Sixth, our last step is to convert the fraction into a mixed fraction. How you do this is to divide the numerator by the denominator. We would set up something like this: 31 ÷ 15 = 2.066667. That decimal in fraction form is 2 1/15, which is our answer.
Answer in fraction form:
Answer in decimal form: