Find 2a- 5bplease help
1 answer:
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The transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>How to transform the logarithmic function?</h3>The parent logarithmic function is
y = log(x)
When shifted left by 4 units, we have:
y = log(x + 4)
When shifted up by 3 units, we have:
y = log(x + 4) + 3
When compressed vertically by 1/3, we have:
y = 1/3(log(x + 4) + 3)
This gives
y = 1/3(log(x + 4)) + 1
When stretched horizontally by 3, we have:
y = 1/3(log(x/3 + 4)) + 1
Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>The transformation of function f(x)</h3>We have:
f(x) = log[-(x – 5)] + 4
Set the radicand greater than 0
-(x - 5) > 0
Divide by -1
x - 5 < 0
Add 5 to both sides
x < 5 -- this represents the domain
A logarithmic function can output any real number.
So, the range is
In the domain, we have:
x < 5
This means that the interval of decrease is
Rewrite as an equation
x = 5 --- this represents the equation of asymptote
Read more about logarithmic functions at:
#SPJ1
Answer:
Option (1)
Step-by-step explanation:
x -2 -1 0 1 2
y 10 2.5 0 2.5 3.0
Ist difference,
= -2.5
= 2.5
= 7.5
2nd difference,
= 5
= 5
= 5
Since 2nd difference is common, given table represents a quadratic equation.
Let the equation is,
y = ax²+ bx + c
For a point (0, 0) passing through the quadratic equation,
0 = c
Therefore, quadratic equation is y = ax² + bx
Since ordered pair (-1, 2.5) passes through the graph of the function,
2.5 = a(-1)² + b(-1)
a - b = 2.5 ------(1)
For another point (1, 2.5)
2.5 = a(1)² + b(1)
a + b = 2.5 ------(2)
By adding equations (1) and (2),
2a = 5
a = 2.5
and from equation (2)→ y = 0
Therefore, equation of the quadratic function given in the table is y = 2.5x²
Option (1) is the answer.