In the xy-plane, the graphs of the linear function and the exponential function E both pass through the points (0,2) and (1,6) The function f is given by f(x) = L(x) - E(x). What is the maximum value of f? A 0.007 B 0.172 C 0.540 D 1.002

GRAPHS AND FUNCTIONS Domain and range of a linear function that models a real-world si... The fuel tank of a certain airplane can hold up to 300 gallons of fuel. Let W be the total weight of the airplane (in pounds). Let F be the total amount of fuel in its tank (in gallons).

Transcribed Image Text: The xy-plane above shows one of the two points of intersection of the (4, 19) graphs of a linear function and a quadratic function. The shown point (v, w) of intersection has coordinates (v, w) . If the vertex of the graph of the quadratic function is at (4, 19), what is the value of v ? (0, 3) (2, – 1) (0, – 9)

Transcribed Image Text: 16 A quadratic function and a linear function are graphed on the same set of axes. Which situation is not possible? 1) The graphs do not intersect. 3) The graphs intersect in two points. 2) The graphs intersect in one point.

y 2- 1- 1 The graphs of the function g and the line y = x are shown in the figure above. The graphs intersect at the points (0, 0), (1, 1), and (2, 2). Which of the following expressions give the area enclosed by the graphs?

Transcribed Image Text: Problem 1: Let p and q be the piecewise linear functions given by their respective graphs in Figure 1 below. Use the graphs to answer the following questions 3- 1- -3 -2 2. 2- -3- Figure 1 (a) Let F(r)= p(q(z)) Determine F(0) and F(3). (b) Find a value of z for which F(r) does not exist. Explain your thinking.

3. A taxi company charges $5.00 for the first quarter mile and $0.60 for each additional quarter mile. Find a linear function F for the total fare in dollars, given x, the number of miles. Graph this function. 4. The height hin feet of a projectile fired up from the ground is given by the function h(t) = −16t² + 128t, where t it the time in ...

Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph. Exponential Functions The exponential function is a type of mathematical function which is used in real-world contexts.

### Key Observations: - Both functions intersect the horizontal line \( y = 1 \) at different \( x \) values. - The graph showcases the intersection of different function types (exponential and linear) with the horizontal line, illustrating concepts of function behavior and intersection points.