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The linear function f(x) = 2x + 3 is in the form f(x) = mx + b. Write down your observations based on the changes made to the parameters and your knowledge of parent functions.

User Tom Fenech
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Final answer:

The linear function f(x) = 2x + 3 represents a straight line with a slope (m) of 2 and a y-intercept (b) of 3. Changes in m and b values determine the line's steepness and position on the graph.

Step-by-step explanation:

The linear function f(x) = 2x + 3 is a specific instance of the standard linear equation y = mx + b, where m represents the slope of the line and b represents the y-intercept. Here, m = 2 indicates that the slope of the line is 2, meaning for each unit increase in x, y increases by 2 units. The b value in our function is 3, which indicates that the y-intercept, the point where the line crosses the y-axis, is at (0, 3). Expressing equations graphically, the line representing f(x) = 2x + 3 will be straight and will angle upwards as it moves from left to right because of the positive slope.

To visualize this, you can construct a table of values by plugging in different x values and calculating the corresponding y values. Plot these (x, y) points on a graph and draw a line through them to see the linear relationship. Thus, variations in the parameters m and b determine the shape and position of the linear graph respectively.

User Carlos Vega
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