{"id":43267,"date":"2025-06-29T17:04:17","date_gmt":"2025-06-29T17:04:17","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=43267"},"modified":"2025-06-29T17:04:18","modified_gmt":"2025-06-29T17:04:18","slug":"determine-algebraically-whether-the-function-is-even-odd-or-neither-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/determine-algebraically-whether-the-function-is-even-odd-or-neither-2\/","title":{"rendered":"Determine algebraically whether the function is even, odd, or neither"},"content":{"rendered":"\n
Determine algebraically whether the function is even, odd, or neither<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Let’s analyze each function algebraically to determine if it’s even, odd, or neither.<\/p>\n\n\n\n
1) f(x)=8×3+3f(x) = 8x^3 + 3f(x)=8×3+3<\/h3>\n\n\n\n
To determine if this function is even, odd, or neither, we need to evaluate f(\u2212x)f(-x)f(\u2212x) and compare it with f(x)f(x)f(x).<\/p>\n\n\n\n
Step 1: Find f(\u2212x)f(-x)f(\u2212x)<\/h4>\n\n\n\n
f(\u2212x)=8(\u2212x)3+3=\u22128×3+3f(-x) = 8(-x)^3 + 3 = -8x^3 + 3f(\u2212x)=8(\u2212x)3+3=\u22128×3+3<\/p>\n\n\n\n
Step 2: Compare f(\u2212x)f(-x)f(\u2212x) with f(x)f(x)f(x)<\/h4>\n\n\n\n
    \n
  • f(x)=8×3+3f(x) = 8x^3 + 3f(x)=8×3+3<\/li>\n\n\n\n
  • f(\u2212x)=\u22128×3+3f(-x) = -8x^3 + 3f(\u2212x)=\u22128×3+3<\/li>\n<\/ul>\n\n\n\n
    Since f(\u2212x)\u2260f(x)f(-x) \\neq f(x)f(\u2212x)\ue020=f(x) and f(\u2212x)\u2260\u2212f(x)f(-x) \\neq -f(x)f(\u2212x)\ue020=\u2212f(x), the function is neither even nor odd.<\/p>\n\n\n\n
    2) f(x)=\u22122×2+4f(x) = -2x^2 + 4f(x)=\u22122×2+4<\/h3>\n\n\n\n
    Again, let’s evaluate f(\u2212x)f(-x)f(\u2212x).<\/p>\n\n\n\n
    Step 1: Find f(\u2212x)f(-x)f(\u2212x)<\/h4>\n\n\n\n
    f(\u2212x)=\u22122(\u2212x)2+4=\u22122×2+4f(-x) = -2(-x)^2 + 4 = -2x^2 + 4f(\u2212x)=\u22122(\u2212x)2+4=\u22122×2+4<\/p>\n\n\n\n
    Step 2: Compare f(\u2212x)f(-x)f(\u2212x) with f(x)f(x)f(x)<\/h4>\n\n\n\n
      \n
    • f(x)=\u22122×2+4f(x) = -2x^2 + 4f(x)=\u22122×2+4<\/li>\n\n\n\n
    • f(\u2212x)=\u22122×2+4f(-x) = -2x^2 + 4f(\u2212x)=\u22122×2+4<\/li>\n<\/ul>\n\n\n\n
      Since f(\u2212x)=f(x)f(-x) = f(x)f(\u2212x)=f(x), this function is even<\/strong>.<\/p>\n\n\n\n
      3) f(x)=4x3f(x) = 4x^3f(x)=4×3<\/h3>\n\n\n\n
      Let\u2019s evaluate f(\u2212x)f(-x)f(\u2212x) for this function.<\/p>\n\n\n\n
      Step 1: Find f(\u2212x)f(-x)f(\u2212x)<\/h4>\n\n\n\n
      f(\u2212x)=4(\u2212x)3=\u22124x3f(-x) = 4(-x)^3 = -4x^3f(\u2212x)=4(\u2212x)3=\u22124×3<\/p>\n\n\n\n
      Step 2: Compare f(\u2212x)f(-x)f(\u2212x) with f(x)f(x)f(x)<\/h4>\n\n\n\n
        \n
      • f(x)=4x3f(x) = 4x^3f(x)=4×3<\/li>\n\n\n\n
      • f(\u2212x)=\u22124x3f(-x) = -4x^3f(\u2212x)=\u22124×3<\/li>\n<\/ul>\n\n\n\n
        Since f(\u2212x)=\u2212f(x)f(-x) = -f(x)f(\u2212x)=\u2212f(x), this function is odd<\/strong>.<\/p>\n\n\n\n
        Summary<\/h3>\n\n\n\n
          \n
        • f(x)=8×3+3f(x) = 8x^3 + 3f(x)=8×3+3 is neither even nor odd.<\/li>\n\n\n\n
        • f(x)=\u22122×2+4f(x) = -2x^2 + 4f(x)=\u22122×2+4 is even.<\/li>\n\n\n\n
        • f(x)=4x3f(x) = 4x^3f(x)=4×3 is odd.<\/li>\n<\/ul>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
          Determine algebraically whether the function is even, odd, or neither The Correct Answer and Explanation is: Let’s analyze each function algebraically to determine if it’s even, odd, or neither. 1) f(x)=8×3+3f(x) = 8x^3 + 3f(x)=8×3+3 To determine if this function is even, odd, or neither, we need to evaluate f(\u2212x)f(-x)f(\u2212x) and compare it with f(x)f(x)f(x). […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-43267","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=43267"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43267\/revisions"}],"predecessor-version":[{"id":43270,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/43267\/revisions\/43270"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=43267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=43267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=43267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}