1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timofeeve [1]
2 years ago
10

Given y = log3(x + 4), what is the range?​

Mathematics
1 answer:
lora16 [44]2 years ago
4 0

Answer:

The range is all real numbers.

The domain is all reals numbers that are greater than -4.

Step-by-step explanation:

y=\log_3(x+4) only exists when x+4 is positive.

You can take the log of a negative or 0 number.

So x+4>0 implies x>-4.  (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 y=\log_3(x+4) is 3^{y}=x+4

We can solve this for x be subtract 4 on both sides:

x=3^y-4

Now here y can be anything; there are no restrictions on the exponent.

Also if you look at the graph of y=\log_3(x+4) 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).

y=3^x-4.

If we look at the domain and range of this we can just swap it to get the domain and range of y=\log_3(x+4).

y=3^x-4 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 (-4,\infty).

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 y=\log_3(x+4):

Domain:  (-4,\infty)

Range : (-\infty,\infty)

You might be interested in
What is 20% tip on a bill of 59.61
Ugo [173]

Answer:

about $12

Step-by-step explanation:

59.61(0.20)=11.922

11.922 rounded up is 12.

ur total bill would be $71.61

5 0
3 years ago
Suppose f(x)=x^2-2 find the graph of f(1/2x)
Scorpion4ik [409]

Answer:

graph g(x)=1/4 x^2 - 2

Step-by-step explanation:

You are to replace x with (1/2x) in the expression x^2-2

So you have (1/2x)^2-2

1/4 x^2-2

Graph some points for g(x)=1/4 x^2-2

The vertex is (0,-2) and the parabola is open up.

I would graph 2 more points besides the vertex

x   |  g(x)                     ordered pairs to graph

-----------                         (-1,-1.75) and (0,-2) and (1,-1.75)

-1        -1.75

0         -2

1         -1.75

3 0
2 years ago
Read 2 more answers
The following table is a function.<br> х -1 5 7 2 6 3 8 4 1 y -3 3 7 -4 5 9 7 1 0
Kruka [31]

Answer:false

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Solve |4 - 2x| = |3x+ 2|.
andreyandreev [35.5K]

Answer:

Step-by-step explanation:4 -2x=3x +2

4-2=3x+2x

2=5x

X=2/5

5 0
2 years ago
Read 2 more answers
PLEASE HURRY!
Yuki888 [10]
Well idk about geometric theorem or how ever. but, because they have the same line aka the same Slope. The other line is parallel to it. Assuming by the statement, -1/3x has another -1/3x of the same Slope.
4 0
3 years ago
Other questions:
  • Whats is 20x6+2x0+1 ????
    14·2 answers
  • 6. Mary and Steve each travel 845 miles. Mary drove an average of 5 mph faster than Steve and completed the trip in one hour's l
    5·1 answer
  • Please help... I'm stuck on number 44 and I can't remember how to do it
    14·2 answers
  • Which shows 42^2 − 38^2 being evaluated using the difference of perfect squares method?
    14·1 answer
  • What is Z +9÷4 = 2 .1
    5·1 answer
  • A typical small bag of colored candies has about 135 candies in it, 27 of which are blue.At this rate,how many blue candies woul
    7·1 answer
  • About 71% of Earth’s surface is covered in water. If the surface area of the Earth is about 196,900,000 square miles, About what
    8·2 answers
  • In the figure above, PQRS is a circle. If PQT and SRT<br>are straight lines, find the value of x.
    14·1 answer
  • Question 17(Multiple Choice Worth 2 points)
    15·1 answer
  • Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!