Exponential Function and Its Properties Quiz

What is the definition of the exponential function with base a?

• f(x) = a^x where a is a real number such that a > 0, a ≠ 1 and x is any real number

• f(x) = a^x where a is a real number such that a < 0, a ≠ 1 and x is any real number

• f(x) = a^x where a is a real number such that a > 0, a = 1 and x is any real number

• f(x) = a^x where a is a real number such that a > 0, a ≠ 1 and x is a positive integer

What happens to the values of an exponential function if the base a is larger than 1?

• Values oscillate with the exponent x

• Values remain constant regardless of the exponent x

• Values decline as the exponent x increases

• Values grow with increasing exponent x

What property is used when solving exponential equations?

• Quadratic property

• Exponential property

• One-to-one property

• Monotonicity property

How can exponential inequalities be solved using the monotonicity property?

• By changing the base of the exponential function

• By reversing the inequality sign

• By comparing the exponents directly

• By dropping the base without changing the direction of the inequality

What is the solution to the inequality (1/27)^4x ≥ 81?

• x > 1

• x ≤ -1/3

• x = 0

• x = 1/2

In the equation 7·4^x - 26 = 2^(2x+1) + 7·4^(x-1), what is the value of x?

• x = 0

• x = 1/2

• x = 3/2

• x = 2

What is the correct solution to the inequality 16^x - 8 < -2^(2x+1)?

• x = 5/4

• x > 1

• x = 1

• x < 1/2

How can the inequality 7 + 4√x - 1/2 > 4√x - 1 + 1 be simplified?

• 1 ≤ x < 5/4

• x = 1

• x < 1/2

• x > 1

What is the correct solution to the equation (1/8)·4√x = 8^(x-1)?

• x = 1

• x = 1/2

• x = 4/9

• x = 0

What is the one-to-one property used for in exponential equations?

• To simplify the equation into one power

• To determine restrictions on the variable

• To reverse the inequality sign

• To compare the exponents directly