Compare
function A: \large y=-3x+2
with
function B:
x y
1 4
2 6
3 8
4 10
a
Function A is decreasing, while function B is increasing AND Function B is steeper
b
Function A is increasing, while function B is decreasing AND Function B is steeper
c
Function A is decreasing and function B is also decreasing AND Function A is steeper
d
Function A is decreasing, while function B is increasing AND Function A is steeper
d
The correct answer is:
d) Function A is decreasing, while function B is increasing AND Function A is steeper.
Here's the explanation:
Function A is described by the equation y = -3x + 2. The coefficient of x, which is -3, is negative. This means that as x increases, y decreases. Therefore, Function A is decreasing.
Function B is represented by a table of values:
x y
1 4
2 6
3 8
4 10
As x increases, y also increases. This indicates that Function B is increasing.
To compare the steepness of the two functions, we can look at the slope of each function. The slope of a linear function is represented by the coefficient of x. The absolute value of the slope gives us the steepness.
In Function A, the slope is -3. In Function B, the change in y for every unit change in x is 2. This means that for every unit increase in x, y increases by 2.
Since the absolute value of -3 is greater than 2, we can conclude that Function A is steeper than Function B.
To compare function A: \(y = -3x + 2\) with function B, let's analyze the properties of both functions.
Function A has the equation \(y = -3x + 2\). This is in the form of a linear equation with a negative slope (-3) and a y-intercept at 2. Since the slope is negative, the function is decreasing. This means that as x increases, y decreases.
To compare Function A with the data points provided for Function B, let's graph both functions on the coordinate plane using the given points for Function B.
Graph for Function B:
\[
\begin{align*}
\text{Point A} & : (1, 4) \\
\text{Point B} & : (2, 6) \\
\text{Point C} & : (3, 8) \\
\text{Point D} & : (4, 10) \\
\end{align*}
\]
By plotting these points, we can observe that as x increases, y also increases. Therefore, Function B is increasing.
Now, let's compare the steepness of both functions. Since Function A has a slope of -3, it means that for every 1 unit increase in x, y decreases by 3 units. This makes Function A steeper.
On the other hand, by looking at the points of Function B, we can observe that for every 1 unit increase in x, y increases by 2 units. This indicates that Function B is less steep than Function A.
Based on this analysis, the correct answer is:
d) Function A is decreasing, while Function B is increasing, AND Function A is steeper.