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.

• Positive Slope

• 
• Negative Slope

• 
• Undefined Slope

• 
• Zero Slope

• 

Tags

CCSS.8.EE.B.5

Construct a linear model for the graph.

Answer explanation

The correct linear model is y=-\frac{1}{2}x-2, as it has a negative slope of -\frac{1}{2} and a y-intercept of -2, matching the graph's characteristics.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Which equation matches the graph

Answer explanation

The graph represents an exponential function, which is best matched by the equation y=2(5^x). The other options are either linear or have a different base, making them inconsistent with the graph's growth pattern.

Tags

CCSS.HSF.LE.A.2

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.

Tags

CCSS.HSF-IF.C.7E

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 curve and do not form straight lines. Therefore, the correct answer is 'Linear'.

Tags

CCSS.HSF-IF.C.7A

• linear

• exponential

• neither

Answer explanation

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

Tags

CCSS.8.F.A.3

• 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 is a constant (5) raised to the variable x. This indicates that the function grows exponentially, not linearly.