Answers Algebra IIFunctions: Part Four

Functions: Part Four — Test Answers

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How does the value of log_2⁡100 compare with the value of the log base 6 of 20 ?

The value of the log base 2 of 100 is about 1 third times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 1 fourth times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 4 times the value of the log base 6 of 20 .

The value of the log base 2 of 100 is about 3 times the value of the log base 6 of 20 .

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What is the true solution to the equation? the natural log of e raised to the natural log x power plus the natural log of e raised to the the natural log of x squared power is equal to 2 ln 8

x is equal to 2

x is equal to 4

x is equal to 8

x is equal to 64

Which expression is equivalent to log sub w the fraction with numerator open paren x squared minus 6 close paren to the 4th power and denominator cube root of x squared plus 8 ?

4 log sub w the fraction with numerator x squared and denominator 1296 minus 1 third log sub w open paren 2 x plus 8 close paren

4 log sub w open paren x squared minus 6 close paren minus 3 log sub w open paren x squared plus 8 close paren

4 log sub w open paren x squared minus 6 close paren minus 1 third log sub w open paren x squared plus 8 close paren

4 times open paren log sub w x squared minus 1 third log sub w open paren x squared plus 8 close paren minus 6 close paren

The range of which function is open paren 2 comma infinity close paren ?

y is equal to 5 raised to the x plus 2 power

y is equal to 5 to the x th power plus 2

y is equal to 2 times open paren 5 to the x th power close paren

y is equal to 2 to the x th power

What is the solution to the given equation? log sub 6 4 x squared minus the log base 6 of x is equal to 2

x is equal to 3

x is equal to 1 over 12

x is equal to 9

x is equal to 3 halves

The equation of the piecewise defined function f of x is shown. What is the value of f of 1 ? f of x equals enlarged left-brace first row x squared plus 1 comma negative 4 less than or equal to x less than 1. Second row negative x squared comma 1 less than or equal to x less than 2. Third row 3 x comma x greater than or equal to 2.

f of 1 is equal to negative 1

f of 1 is equal to 2

f of 1 is equal to 3

f of 1 is equal to negative 2

What is the range of the function y is equal to 2 e to the x th power minus 1 ?

all real numbers less than negative 1

all real numbers less than 1

all real numbers greater than 1

all real numbers greater than negative 1

What is the solution to the equation 2 raised to the x plus 4 power minus 12 is equal to 20 ?

x is equal to 1

x is equal to 2

x is equal to 9

x is equal to 0

What is the domain of y is equal to log sub 4 of open paren x plus 3 close paren ?

all real numbers less than negative 3

all real numbers greater than 3

all real numbers greater than negative 3

all real numbers less than 3

What is the value of the log base 625 of 5 ?

negative 4

1 fourth

negative 1 fourth

What is the approximate value of the log base 6 of 25 ?

0 point 5 5 7

0 point 2 3 3

0 point 6 2 0

1 point 7 9 6

Calvin deposits 400 dollars in a savings account that accrues 5 percent interest compounded monthly. After c years, Calvin has 658 point 8 0 dollars Makayla deposits 300 dollars in a different savings account that accrues 6 percent interest compounded quarterly. After m years, Makayla has 613 point 0 4 dollars What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

Makayla invests her money 1 year longer.

Makayla invests her money 2 years longer.

Calvin invests his money 1 year longer.

Calvin invests his money 2 years longer.

Which graph represents an exponential decay function?

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at the origin (0 comma 0) and extends into the first quadrant. The curve is continuously increasing and appears concave down. It passes through (1 comma 1), (3 comma 2), and (8 comma 3).

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 1 comma 2), (negative 2 comma 4), (negative 3 comma 8), (0 comma 1), (1 comma 0 point 5), and (2 comma 0 point 2 5). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches positive infinity.

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), (2 comma 4) and (3 comma 8). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches negative infinity.

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at approximately (0 comma 0) and extends to the right in fourth quadrant. The curve is continuously decreasing and it passes through approximately (1 comma negative 1), (4 comma negative 2), and (9 point 5 comma negative 3).

Which expression is equivalent to log sub 12 the fraction with numerator x to the 4th power square root of x cubed minus 2 end root and denominator open paren x plus 1 close paren to the 5th power ?

4 log sub 12 x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 open paren x times 1 close paren

4 log sub 12 x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 open paren x plus 1 close paren

4 log sub 12 x plus 1 half log sub 12 the fraction with numerator x cubed and denominator 2 minus 5 log sub 12 x plus the log base 12 of 1

the log base the log base 12 of 4 of x plus 1 half log sub 12 open paren x cubed minus 2 close paren minus 5 log sub 12 x plus 1

Which piecewise relation defines a function?

y equals enlarged left-brace first row x squared comma x less than negative 2. Second row 0 comma negative 2 less than or equal to x less than or equal to 4. Third row negative x squared comma x greater than or equal to 4.

y equals enlarged left-brace first row negative 3 x comma x less than negative 4. Second row 3 comma negative 5 less than x less than 1. Third row 2 x comma x greater than or equal to 1.

y equals enlarged left-brace first row x squared comma x less than or equal to negative 2. Second row 4 comma negative 2 less than x less than or equal to 2. Third row x squared plus 1 comma x greater than or equal to 2.

y equals enlarged left-brace first row negative 3 x comma x less than negative 2. Second row 3 comma 0 less than or equal to x less than 4. Third row 2 x comma x greater than or equal to 4.

A population of insects increases at a rate of 1 point 5 percent per day. About how long will it take the population to double?

46 point 6 days

66 point 7 days

2 point 5 days

5 point 0 days

If f of x is equal to 3 lfloor x minus 2 rfloor , what is f of 5 point 9 ?

If you are given the graph of h of x is equal to the log base 6 of x , how could you graph m times x is equal to log sub 6 of open paren x plus 3 close paren ?

Translate each point of the graph of h x 3 units right.

Translate each point of the graph of h x 3 units down.

Translate each point of the graph of h x 3 units up.

Translate each point of the graph of h x 3 units left.

Which of the following is true about the base b of a logarithmic function?

b is greater than 0 and b is not equal to 1

b is greater than 0 and b is equal to 1

b is less than 0 and b is equal to 1

b is less than 0 and b is not equal to 1

What is the solution of log sub 2 of open paren 3 x minus 7 close paren is equal to 3 ?

1 third

16 thirds

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Functions: Part Four — Test Answers

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