91Ó°ÊÓ

A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this point of contact. Write an equation in point-slope form for the line tangent to the circle whose equation is \(x^{2}+y^{2}=25\) at the point (3,-4).

The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the computer, \(f^{\circ}\) g or \(g \circ f\) ? Explain.

Here is the Federal Tax Rate Schedule \(X\) that specifies the tax owed by a single taxpayer for a recent year. (TABLE CANNOT COPY) The preceding tax table can be modeled by a piecewise function, where \(x\) represents the taxable income of a single taxpayer and \(T(x)\) is the tax owed: $$T(x)=\left\\{\begin{array}{ccc} 0.10 x & \text { if } & 0379,150 \end{array}\right.$$ Use this information to solve. Find and interpret \(T(20,000)\)

Here is the Federal Tax Rate Schedule \(X\) that specifies the tax owed by a single taxpayer for a recent year. (TABLE CANNOT COPY) The preceding tax table can be modeled by a piecewise function, where \(x\) represents the taxable income of a single taxpayer and \(T(x)\) is the tax owed: $$T(x)=\left\\{\begin{array}{ccc} 0.10 x & \text { if } & 0379,150 \end{array}\right.$$ Use this information to solve. Find and interpret \(T(50,000)\)

Determine whether statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every line in the rectangular coordinate system has an equation that can be expressed in slope-intercept form.

What is the graph of a function?

Find the coefficients that must be placed in each shaded area so that the function's graph will be a line satisfying the specified conditions. ___ \(x+\) ___ \(y-12=0 ; x\) -intercept \(=-2 ; y\) -intercept \(=4\)

For people filing a single return, federal income tax is a function of adjusted gross income because for each value of adjusted gross income there is a specific tax to be paid. By contrast, the price of a house is not a function of the lot size on which the house sits because houses on same-sized lots can sell for many different prices. a. Describe an everyday situation between variables that is a function. b. Describe an everyday situation between variables that is not a function.

What is a piecewise function?

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$h(x)=2-x^{\frac{2}{5}}$$