Constructing Functions from Graphs Warmup

When linear functions are graphed they have a certain type of slope.

Match the graph with the correct type of slope.

• Undefined Slope

• 
• Negative Slope

• 
• Zero Slope

• 
• Positive Slope

• 

Construct a linear model for the graph.

Answer explanation

The correct linear model is identified by its slope and y-intercept. The equation y=-\frac{1}{2}x-2 has a slope of -\frac{1}{2} and a y-intercept of -2, matching the graph's characteristics, making it the correct choice.

Which equation matches the graph

Answer explanation

The graph represents an exponential function. The correct equation, \(y=2(5^x)\), indicates a base of 5, which matches the growth rate shown in the graph. The other options do not fit the exponential behavior observed.

The graph of this function is a curve going up really fast or down really fast. 

• Linear 

• Exponential

• Neither

Answer explanation

The function described has a graph that increases or decreases rapidly, characteristic of exponential functions. Linear functions increase or decrease at a constant rate, not rapidly.

The graph of this function is a straight line.

• Linear

• Exponential

• Neither

Answer explanation

The graph of a linear function is a straight line, which means it has a constant rate of change. In contrast, exponential functions produce curves. Therefore, the correct answer is Linear.

• linear

• exponential

• neither

Answer explanation

The function f(x) = 3x - 7 is linear because it can be expressed in the form f(x) = mx + b, where m is the slope (3) and b is the y-intercept (-7). It represents a straight line, confirming it is linear.

• linear

• exponential

• neither

Answer explanation

The function f(x) = (1/3)·5^x is exponential because it has the form a·b^x, where b (5) is a constant base raised to the variable exponent x. Thus, the correct choice is exponential.