Four ninths plus one ninth?
2 answers:
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Answer:
B the range, the x- and y-intercept
Step-by-step explanation:
the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).
but the range changes, as for the original function y could only have positive values - even for negative x.
the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.
the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.
the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.
the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.
the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)
Answer:
The range is all real numbers.
The domain is all reals numbers that are greater than -4.
Step-by-step explanation:
only exists when
is positive.
You can take the log of a negative or 0 number.
So implies
. (I just subtract 4 on both sides.)
So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.
Now the range. The range is where the curve exist for the y-values.
The equivalent exponent form of is
We can solve this for x be subtract 4 on both sides:
Now here y can be anything; there are no restrictions on the exponent.
Also if you look at the graph of you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).
Let's think about the inverse I found above a little more (I'm going to swap x and y).
.
If we look at the domain and range of this we can just swap it to get the domain and range of .
is an exponential function of 3^x that has been moved down 4 units.
The range since it has been moved down 4 units is .
The domain of an exponential function is all real numbers. There are no restrictions on what you can plug in for x.
So swapping these to find the domain and range of :
Domain:
Range :