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3 years ago

Which logarithmic function has a y-intercept?

2 answers:

4 0

Hello :
answer A. f(x) = log(x + 1) – 1 because f(o) exist : f(o) = log(0+1)-1 = log(1)-1 =-1 ...log1=0
a y-intercept is : -1

Elza [17]3 years ago

4 0

Answer:

f(x) = log(x + 1) – 1 ha a y-intercept.

Step-by-step explanation:

Y-intercept is a point where the graph intersects the y-axis. And at y-axis the x-coordinate is zero.

Hence, for y-intercept, x=0

All the given functions are logarithm and we will substitute x =0, to find the y-intercept.

Logarithm function is defined only when x>0.

All the functions except the first one are undefined for x =0. Let us see how.

For B, plug x=0

f(x) = log0 + 1

Since, log 0 is undefined, hence there is no y-intercept.

For C, plug x=0

f(x) = log(0-1) + 1

f(x)=log (-1) +1

Since, log -1 is undefined, hence there is no y-intercept.

For D, plug x=0

f(x) = log(0-1) - 1

f(x)=log (-1) -1

Since, log -1 is undefined, hence there is no y-intercept.

Hence all these have no y-intercept.

Now check for A

Set x=0

f(0) = log(0 + 1) – 1

=log1 -1

=0-1

=-1

Hence, the function has a y-intercept of -1.

Thus, f(x) = log(x + 1) – 1 ha a y-intercept.

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3 years ago

Does each equation represent exponential decay or exponential growth?

lisov135 [29]

Answer:

1. $H = 5.9(0.82)^{t}$ . Exponential decay function.

2. $y = 0.8(3.6)^{t}$ . Exponential growth function.

3. $f(t) = 0.72(15)^{t}$ . Exponential growth function.

4. $A = \frac{4}{9} (8)^{t}$ . Exponential growth function.

5. $A = (\frac{4}{3})^{t}$ . Exponential growth function.

6. $H = \frac{7}{2} (\frac{5}{6} )^{t}$ . Exponential decay function.

7. g(x) = 0.3(x). Not an exponential function.

Step-by-step explanation:

1. $H = 5.9(0.82)^{t}$ . This is an exponential decay function.

As the value of t increases H-value decreases.

2. $y = 0.8(3.6)^{t}$ . This is an exponential function of growth.

As the value of t increases y-value also increases.

3. $f(t) = 0.72(15)^{t}$ . This is an another example of exponential growth function.

As the value of t increases f(t)-value also increases.

4. $A = \frac{4}{9} (8)^{t}$ . This is again an example of exponential growth function.

As the value of t increases A-value also increases.

5. $A = (\frac{4}{3})^{t}$ . This is again an example of exponential growth function.

As the value of t increases A-value also increases.

6. $H = \frac{7}{2} (\frac{5}{6} )^{t}$ . This is another an example of exponential decay function.

As the value of t increases, H-value decreases.

7. g(x) = 0.3(x). This is a non-exponential function. (Answer)

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4 years ago

What is 3/30 simplified

Otrada [13]

Your answer will be 1/10. you divide 3 by the numerator and denominator

6 0

3 years ago

Read 2 more answers

While testing a new vaccine, a lab technician noticed that the number of bacteria reduced by half every minute. How long does it

ANTONII [103]

As we know that
x=x0*[1/2]n
putting the values
375=3000*[1/2]n
375/3000=[1/2]n
1/8=[1/2]n
simplify
[1/2]3=[1/2]n
by cancelling them
so n=3
so it will take 3 minutes
hope it helps

7 0

3 years ago

In triangle MNO shown below, segment NP is an altitude:

Effectus [21]

Answer: C. Definition of an Altitude

Step-by-step explanation:

Given: In triangle MNO shown below, segment NP is an altitude from the right angle.

Let ∠MNP=x

Then ∠PNO=90°-x

Therefore in triangle MNO,

∠MPN=∠NPO =90° [by definition of Altitude]

[Definition of altitude : A line which passes through a vertex of a triangle, and joins the opposite side forming right angles. ]

Now using angle sum property in ΔMNP

∠MNP+∠MPN+∠PMN=180°

⇒x+90°+∠PMN=180°

⇒∠PMN=180°-90°-x

⇒∠PMN=90°-x

Now, in ΔMNO and ΔPNO

∠PMN=∠PNO=90°-x

and ∠MPN=∠NPO =90° [by definition of altitude]

Therefore by AA similarity postulate, we have

ΔMNO ≈ ΔPNO

5 0

3 years ago