Example Question - function values
Here are examples of questions we've helped users solve.
Completing a Function Table
<p>Para completar la tabla de la función \( f(x) = -x^2 - 8x + 7 \), sustituya los valores de x en la función y calcule los valores correspondientes de \( f(x) \).</p> <p>Para x = 0:</p> <p>\( f(0) = -(0)^2 - 8(0) + 7 = 7 \)</p> <p>Para x = 1:</p> <p>\( f(1) = -(1)^2 - 8(1) + 7 = -1^2 - 8 + 7 = -1 - 8 + 7 = -2 \)</p> <p>Para x = 2:</p> <p>\( f(2) = -(2)^2 - 8(2) + 7 = -2^2 - 16 + 7 = -4 - 16 + 7 = -13 \)</p> <p>Para x = 3:</p> <p>\( f(3) = -(3)^2 - 8(3) + 7 = -3^2 - 24 + 7 = -9 - 24 + 7 = -26 \)</p> <p>Para x = 4:</p> <p>\( f(4) = -(4)^2 - 8(4) + 7 = -4^2 - 32 + 7 = -16 - 32 + 7 = -41 \)</p> <p>Para x = 5:</p> <p>\( f(5) = -(5)^2 - 8(5) + 7 = -5^2 - 40 + 7 = -25 - 40 + 7 = -58 \)</p> <p>Para x = 6:</p> <p>\( f(6) = -(6)^2 - 8(6) + 7 = -6^2 - 48 + 7 = -36 - 48 + 7 = -77 \)</p> <p>Por lo tanto, la tabla completa sería:</p> <p>\[ \begin{align*} x & : 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ f(x) & : 7 & -2 & -13 & -26 & -41 & -58 & -77 & - & 7 \\ \end{align*} \]</p> <p>Nota: El valor especificado para \( x = 7 \) no está dado en la imagen y no se calcula aquí porque normalmente completaríamos la tabla con valores consecutivos de x y, en este caso, el valor para \( x = 8 \) ya nos lo han proporcionado. Sin embargo, si se desea calcular \( f(7) \), se sigue el mismo procedimiento que con los otros valores de x.</p>
Challenging Trigonometric Identities and Proofs
<p>The image is not clear enough to provide a full solution to a specific problem, but I will provide a general approach to solving trigonometric identities and proofs.</p> <p>1. Identify the trigonometric identity or equation you need to prove or solve.</p> <p>2. Use known trigonometric identities such as sin^2(x) + cos^2(x) = 1, tan(x) = sin(x)/cos(x), and 1 + tan^2(x) = sec^2(x) to manipulate the equation.</p> <p>3. Substitute trigonometric functions with equivalent expressions when possible.</p> <p>4. Factor and simplify the expressions where necessary.</p> <p>5. Check if the obtained equation satisfies the identity or theorem you are proving.</p> <p>Due to the unclear nature of the image, this is a general method for tackling trigonometric problems rather than a solved equation from the image.</p>
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