DOMAIN AND RANGE. WARM UP Let’s say we use the function T=(1/4)R+40 to model relationship between the temperature, T, and a cricket’s ‘chirp’ rate, R.

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Presentation transcript:

DOMAIN AND RANGE

WARM UP Let’s say we use the function T=(1/4)R+40 to model relationship between the temperature, T, and a cricket’s ‘chirp’ rate, R. What are reasonable input and output values for this relationship?

DOMAIN AND RANGE If Q = f(t), then The domain of f is the set of input values, t, which yield an output value. The range of f is the corresponding set of output values, Q.

DOMAIN IS ALL REAL NUMBERS. UNLESS…

FINDING DOMAIN AND RANGE FROM A GRAPH

IN CLASS FUN p.72 # 5-12, 15-18, 25, 27-30

WARM UP A high diver jumps off a 10 meter springboard. For h in meters and t in seconds after the diver leaves the board, her height above the water is in the figure below and given by the equation (a)Find and interpret the domain and range of the function (in this setting) and the intercepts of the graph. (b)Identify the concavity (we will talk about this)

WARM UP (a)Find and interpret the domain and range of the function and the intercepts of the graph. Using the quadratic formula, we get that h=0 at t=2.462 seconds Domain is 0 ≤ t ≤ Range is approximately 0 ≤ f(t) ≤ Vertical intercept (like the y-intercept) is f(0)=10 meters (b)Identify the concavity (we will talk about this)

QUADRATIC FORMULA

CONCAVITY If f is a function whose rate of change increases (gets less negative or more positive as we move from left to right), then the graph of f is concave up. Another way we can say the same thing is that it bends upwards. If f is a function whose rate of change decreases (gets less positive or more negative as we move from left to right), then the graph of f is concave down. The graph bends downward.

CONCAVITY

PRACTICE WITH QUADRATICS Use your notebooks to record your thoughts. For each of the problems on this quadratics exercise, I would like for you to also - Find the domain and range of the function - Identify whether the function is concave up or concave down - Where the function is increasing or decreasing (use interval notation)

LINEAR VS. EXPONENTIAL p. 120 #1-19