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- Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = (x - 5)^2 - 4
Problem 26
- Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=10x^6-x^5+2x-2
Problem 26
- Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. -2+√5, -2-√5, -2, 1
Problem 26
Problem 27
Solve each problem. Circumference of a CircleThe circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11 in.
Problem 27
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (x - 4)(2x + 3)(3x - 1) ≥ 0
- Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=3+2x-4x^2-5x^10
Problem 27
- Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -1/2 (x + 1)^2 - 3
Problem 27
- Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=7+2x-5x^2-10x^4
Problem 28
- Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -3 (x - 2)^2 +1
Problem 28
Problem 29
Solve each problem. Resistance of a WireThe resistance in ohms of a platinum wire temperature sensor varies directly as the temperature in kelvins (K). If the resistance is 646 ohms at a temperature of 190 K, find the resistance at a temperature of 250 K.
Problem 29
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (x - 3)(x - 4)(x - 5)^2 ≤ 0
Problem 29
Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once.
- Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = x^2 + 6x + 5
Problem 30
- Find all rational zeros of each function. ƒ(x)=8x^4-14x^3-29x^2-4x+3
Problem 30
Problem 31
Solve each problem. Distance to the HorizonThe distance that a person can see to the horizon on a clear day from a point above the surface of Earth varies directly as the square root of the height at that point. If a person 144 m above the surface of Earth can see 18 km to the horizon, how far can a person see to the horizon from a point 64 m above the surface?
- Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x-k) q(x) + r. ƒ(x) = 3x^4 + 4x^3 - 10x^2 + 15; k = -1
Problem 31
Problem 31
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. -(x - 3)(x - 4)2 (x - 5) > 0
- Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=-2x(x-3)(x+2)
Problem 31
- Match the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=1/(x+4)
Problem 31
- Factor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=x^4+2x^3-7x^2-20x-12; k=-2 (multiplicity 2)
Problem 31
Problem 31a
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=3x^3-8x^2+x+2 between -1 and 0
Problem 31b
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=3x^3-8x^2+x+2 between 2 and 3
Problem 31c
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=3x^3-8x^2+x+2 Find the zero in part (b) to three decimal places.
- Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=-x(x+1)(x-1)
Problem 32
- Factor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=2x^4+x^3-9x^2-13x-5; k=-1 (multiplicity 3)
Problem 32
Problem 32a
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=4x3-37x2+50x+60 between 2 and 3
Problem 32b
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=4x3-37x2+50x+60 between 7 and 8
Problem 32c
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=4x^3-37x^2+50x+60 Find the zero in part (b) to three decimal places.
- For each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=x^3-x^2-4x-6; 3
Problem 33
- For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^2 + 5x+6; k = -2
Problem 33
