Gr 10 Math Ch 5: Exponential Function

What is the domain of an exponential function of the form $y = ab^x + q$?

Only integers

All real values of $x$ (correct)

All negative real numbers

All positive real numbers

For the function $y = -2(3^x) + 1$, which direction does the graph curve?

It is a straight line

Downwards (correct)

Upwards

Sideways

What effect does a positive value of $q$ have on the graph of $y = ab^x + q$?

Shifts the graph vertically upwards (correct)

Shifts the graph to the right

Shifts the graph vertically downwards

Shifts the graph to the left

If $y = 5(2^x) - 3$, what is the horizontal asymptote of this function?

$y = -3$ Signup and view all the answers

For an exponential function to represent decay, which condition must be true?

$0 Signup and view all the answers

What is the y-intercept of the function $y = 4(3^x) - 2$?

-2 Signup and view all the answers

If $y = ab^x + q$ and $a = -1$ with $b = rac{1}{2}$, what type of graph does the function create?

Exponential decay that opens downwards Signup and view all the answers

For the function $y = 3(5^x) + 4$, which statement about the graph is true?

It has a horizontal asymptote at $y = 4$ Signup and view all the answers

What is the effect of the parameter $a$ on the orientation of the graph of an exponential function?

It determines whether the graph curves upwards or downwards. Signup and view all the answers

What is the y-intercept of the function expressed as $y = 7(1.5^x) - 4$?

3 Signup and view all the answers

Which horizontal line represents the asymptote for the function $y = -3(2^x) + 5$?

y = 5 Signup and view all the answers

For the exponential function $y = -4(3^x)$, how does the sign of $b$ affect the function?

It has no effect on the function since $b$ must always be positive. Signup and view all the answers

In the exponential function $y = 5(0.5^x) + 2$, what type of behavior does the graph represent?

Exponential decay Signup and view all the answers

What characteristic describes the range of an exponential function where $a < 0$?

The range is less than the horizontal asymptote value. Signup and view all the answers

When sketching the graph of an exponential function, what is considered the first step?

Identify the sign of parameter $a$. Signup and view all the answers

If an exponential function has a $q$ value of -3, what can be inferred about its horizontal asymptote?

It is at y = -3. Signup and view all the answers

What happens to the horizontal asymptote of the graph when the parameter $q$ is modified?

It shifts vertically by $q$ units. Signup and view all the answers

In the function $y = -5(2^x) + 3$, which characteristic indicates the graph curves downwards?

The parameter $a$ being negative. Signup and view all the answers

For an exponential function to exhibit growth, which condition must the base $b$ meet?

It must be greater than 1. Signup and view all the answers

Which of the following describes the range of an exponential function where $a > 0$?

The range is $ ext{greater than } q$. Signup and view all the answers

When sketching the graph of $y = 3(0.7^x) - 1$, what is the first characteristic to determine?

The horizontal asymptote. Signup and view all the answers

What describes the range of the function $y = -2(1.5^x) + 4$?

The function values are below 4. Signup and view all the answers

For the function $y = 0.5(4^x) + 2$, how does the value of $b$ affect the growth rate?

A higher value results in faster growth. Signup and view all the answers

Which situation would lead to an exponential decay graph?

$a < 0$ and $0 Signup and view all the answers

How does changing the value of $a$ affect the graph of the function $y = ab^x + q$?

It affects whether the graph curves upwards or downwards. Signup and view all the answers

Which of the following conditions must be met for the graph of $y = ab^x + q$ to possess a horizontal asymptote?

The function must include a vertical shift ($q$). Signup and view all the answers

In an exponential function given by $y = ab^x + q$, what impact does setting $b$ to a value between 0 and 1 have?

The function will always exhibit exponential decay. Signup and view all the answers

Which of the following statements about the y-intercept of an exponential function $y = ab^x + q$ is correct?

It can be determined using the formula $f(0) = a + q$. Signup and view all the answers

What does the presence of a negative value for $a$ indicate about the graph of the function $y = ab^x + q$?

The graph will always be below the horizontal asymptote. Signup and view all the answers

For an exponential function to exhibit growth, which condition regarding the base $b$ must be satisfied?

$b$ must be greater than 1. Signup and view all the answers

When analyzing the function $y = 3(2^x) - 5$, what impact does $q = -5$ have on the graph?

It shifts the graph vertically downwards by 5 units. Signup and view all the answers

What characteristic of the graph can be determined by the intercepts of the function $y = ab^x + q$?

Both intercepts give information about the growth or decay of the function. Signup and view all the answers